This paper identifies endogenous social effects in mathematics test performance for eighth graders in rural Bangladesh using information on arsenic contamination of water wells at home as an instrument. In other words, the identification relies on variation in test scores among peers owing to exogenous exposure to arsenic contaminated water wells at home. The results suggest that the peer effect is significant, and school selection plays little role in biasing peer effects estimates.Tertiary Education,Education For All,Teaching and Learning,Primary Education,Secondary Education

Asadullah, Mohammad Niaz

Chaudhury, Nazmul

English

Research Papers in Economics

Po l i c y  Re s e a R c h Wo R k i n g  Pa P e R 4508
Social Interactions and Student 
Achievement in a Developing Country:
An Instrumental Variables Approach
Mohammad Niaz Asadullah
Nazmul Chaudhury
The World Bank
South Asia Region
Human Development  Unit
February 2008
WPS4508
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dProduced by the Research Support Team
Abstract
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development 
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the 
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those 
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its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Po l i c y  Re s e a R c h Wo R k i n g  Pa P e R 4508
This paper identifies endogenous social effects in 
mathematics test performance for eighth graders in rural 
Bangladesh using information on arsenic contamination 
of water wells at home as an instrument. In other 
words, the identification relies on variation in test scores 
This paper—a product of the South Asia Human Development Unit—is part of a larger effort in the unit to promote 
research and impact evaluations in the education sector of the South Asia Region. Policy Research Working Papers are also 
posted on the Web at http://econ.worldbank.org. The author may be contacted at nchaudhury@worldbank.org.  
among peers owing to exogenous exposure to arsenic 
contaminated water wells at home. The results suggest 
that the peer effect is significant, and school selection 
plays little role in biasing peer effects estimates.  
Social interactions and student achievement in a developing country: An 
instrumental variables approach 
 
 
Mohammad Niaz Asadullah 
Department of Economics, University of Reading Business School, UK 
ESRC Centre on Skills, Knowledge and Organizational Performance, Oxford, UK. 
 
Nazmul Chaudhury 
The World Bank 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Address for correspondence: 
 
Dr M Niaz Asadullah 
Department of Economics, Business School, University of Reading,  
HUMSS Building, PO Box 218, Whiteknights, Reading RG6 6AA, UK 
Tele: +44-7737045186; Fax +44-118 975 0236; Email: m.asadullah@reading.ac.uk. 
 
 
 
 
 
 
 
 
The authors would like to thank Michelle Riboud for her valuable comments.  The authors 
would also like to thank Sayed Rashed Al-Zayed Josh for his assistance with data processing.  
Note that this study does not represent the views of the World Bank or the Governments 
they represent.  
 
 1. Introduction 
A well-known challenge in studies on the influence of peers in children’s outcomes is that of 
identification of social effects. According to Manski (1993), peer effect can be explained 
by two distinct hypotheses. The hypothesis of “endogenous social effect” states that 
individual behavior is motivated by the average behavior of others in a reference group. 
Second is the hypothesis of “contextual effect”: an individual’s behavior in the group 
varies with the exogenous characteristics of the reference population. In addition to the 
conventional problem of omitted variable related bias, identification of an endogenous social 
effect is complicated by the “reflection problem”: mean behavior of peers is also affected by 
the individual’s own behavior. 
  Although there exists is a sizable empirical literature on social interactions in school 
participation and attainment decisions, research exploring peer effects on student 
achievement, particularly using developing country data, is limited
1.  Extant studies employ a 
variety of techniques to resolve the identification problems such as experimental design (e.g. 
Bobonis and Finan, 2007), school fixed-effects (Arcidiacono and Nicholson, 2005; 
Ammermueller and Pischke, 2006) and instrumental variable approach. Two recent studies 
have attempted to resolve the issue of identification within an instrumental variable 
framework. Cipollone and Rosolia (2007) use data on earthquake shocks in Italy and the 
subsequent relief from military training of males to identify social effects on school 
completion of Italian females
2. On the other hand, Lalive and Cattaneo (2006) identify the 
peer effect on school attendance decision for a sample of children in Mexico who were 
ineligible for a randomly targeted school grant program. Identification is established using 
variation in mean schooling of peers due to exposure to the school grant by a fraction of the 
peers. In both studies, existence of an exogenous shock affecting the schooling outcome of a 
sub-sample of peers has been central for the purpose of identification. We note that in rural 
Bangladesh, a significant part of the population has been exposed to arsenicosis -- intake of 
arsenic-contaminated drinking water at home – which has serious health and learning 
implications
3. Continuous drinking from arsenic-laced wells is highly cancerous and causes 
                                                 
1 See Soetevent (2006) for an extensive review. 
2 Boys high school graduation rate is instrumented with the exemption from compulsory military service. 
3 The extent of the crisis is nation-- according to Rohde (2005), as many as 20 million Bangladeshis have been 
drinking groundwater water contaminated with naturally occurring inorganic Arsenic for nearly over two 
decades (see Geen, Ahmed and Madajewicz (2005) for a detailed account of the crisis). 
  2various other health disorders including birth complications. Arsenicosis is also found to be 
negatively associated with learning outcomes in rural Bangladesh (Asadullah and Chaudhury, 
2007a
4; Wasserman et al., 2004) and elsewhere (ASTDR, 2005). In this paper, therefore, we 
use information on arsenicosis among peers to construct an instrument for the mean test 
score of peers and adopt an instrumental variable approach to estimate the peer effect 
modelled as an endogenous social effect
5. 
2. Methodology 
We adopt a simple OLS regression model for test scores with controls for various demand 
and supply side factors where individual schooling achievement varies linearly with mean 
achievement in the group and with other personal and family attributes that may be common 
across all group members. Such simple linear-in-means regression with group (school) 
average variables can be specified as follows: 
[ ] bi b bi bi b bi SS x β δα ε =Ε + + +        ( 1 )  
where, Sbi is test score and Eb[Sbi] is the corresponding group level (i.e. mean test score of 
children in b-th school) analogue; xbi  proxies for individual specific characteristics (e.g. 
gender, religion, parental education etc.) of i-th child in b-th school
6.  αb  is unobserved 
heterogeneity common across children within the b-th school and εbi is a random error term. 
We assume away any contextual social effect.   
  δ in equation (1) is a measure of endogenous social effect. Given that xbi are pre-
determined, contextual effects are exogenous in educational production. Poor control of αb -
- the “correlated effect” -- may lead to bias in the estimated endogenous and contextual 
effects. However, even if no correlated effects are present in the data, β is not identified in a 
simple linear regression (unless additional assumptions are made), due to what Manski calls 
“reflection problem”. Data on outcomes do not reveal whether group behavior actually 
affects individual behavior or group behavior is simply an aggregation of individual behavior. 
So, the endogenous effect can not be separated from other contextual effects. To identify β, 
                                                 
4 Looking at test score by arsenic pollution status of tube well at home, children from affected households have 
systematically lower maths score. Most importantly, Asadullah and Chaudhury find that these differences in 
raw data prevail even when they account for various conventional determinants of school performance and 
subjective well being such as socio-economic condition of the family, personal attributes, schooling history and 
school attributes (including arsenic contamination status of tube wells at secondary school). 
5 We do not consider contextual effects. It is not uncommon to exclusively focus on endogenous effect. For 
example, see Evans et al. (1992).  
6 In the calculation of school averages we take out the index child.  
  3the endogenous social effect parameter, we need data on an exogenous shock which affect 
schooling of some but not all school peers. To this end, we use data on “fraction of peers 
exposed to arsenic contaminated water-wells at home” as an instrument for Eb[Sbi] and 
follow an the instrumental variable approach to estimate equation (1) to resolve the 
identification problem. 
3.  Data and survey description 
The data used in this paper has been collected in 2005 as part of a larger study to assess 
school quality in rural Bangladesh. The primary sampling unit of the survey was chosen to be 
unions
7. To account for regional variation in school participation rate and so on, 60 unions 
were selected with proportional allocation from 6 divisions in the country. In the second 
step, all secondary (recognized secular and religious) schools in each of the sample unions 
were selected for data collection. In total, 321 schools could be identified in the 60 unions 
(or school catchment areas). A mathematics test was administered to all students in enrolled 
in grade 8 in our sample schools, who were present on the day of the survey
8.  Each student 
taking the test was asked to answer a number of questions relating to their family 
background and pre-secondary school history. To identify arsenic-exposure, we asked 
sample pupils whether there was a tube-well at home and if so, whether they were arsenic 
contaminated
9.  13% of sample kids belong to households with arsenic contaminated tube 
wells (see Asadullah and Chaudhury (2007a) for a descriptive discussion of the sample by 
arsenic exposure).  
4. Results 
Table 1 reports the regression estimates of the endogenous social effect. Certain parts of 
rural Bangladesh have remained less unexposed to ground water poisoning of arsenic leading 
to spatial variation in arsenicosis. Therefore, the regressions always condition on a large 
number of region dummies. We start with a parsimonious model, regressing individual test 
score on mean test score of peers (model 1). Correcting for endogeneity of peer variable 
returns a slightly smaller albeit significant estimate of social effect (model 2). Next, we 
                                                 
7 Union is an administrative unit bigger than a village but smaller than thana/upazila. 
8 The test instrument was constructed by adopting 20 items previously used in the Trends in International 
Mathematics and Science Study (TIMSS), 1999; see Asadullah et al. (2007b) for details.  
9 By the year 2004, the Government of Bangladesh had completed a nationwide screening of tube wells in rural 
areas. Following this exercise, wells identified as contaminated were painted red whilst those ascertained as 
being safe were painted green (BAMWSP, 2005). Therefore, contamination status was ascertained by asking kids 
whether tube well at home was painted red or green.  
  4exploit the richness of the data and control for various individual, household and school 
level (past as well as contemporaneous) correlates of learning (model 3). For this 
specification, instrumental variable estimate of peer effect returns a coefficient of 0.70 
(model 4). The size of the coefficient is slightly reduced to 0.65 when we additionally treat 
school type (whether an Islamic school) as endogenous (model 5) (for details, see Asadullah 
et al., 2007b).  In all cases, however, our estimate of endogenous social effect remains 
statistically significant.  
 
Table 1: OLS and 2SLS estimates of peer effects, full sample 
  
 (1) (2) (3) (4)    (5)
 OLS 2SLS
1st 
 stage OLS 2SLS 
1st  
stage 2SLS
1st 
stage
Mean maths score of peers  0.960 0.713 0.957 0.700    0.657
 (87.01)** (2.25)* (82.33)** (2.26)*   (2.10)*
Fraction of peers with arsenic-
affected homes tubewells  -0.037   -0.041  -0.040
 (3.35)**   (3.47)**  (3.44)**
N  7710 7710 7710 7710 6595 6595  6595 6595
Control for family and school 
attributes ? 
  No  No  No  Yes Yes  Yes  Yes Yes
Regional FEs?  Yes Yes Yes Yes Yes Yes  Yes Yes
F-test stat  11.23 12.05    11.85
Overid --- ---    0.21
R-squared 0.48 0.43 0.02 0.50 0.45 0.08  0.44 0.08
Note: Absolute value of t statistics in parentheses. + significant at 10%; * significant at 5%; ** significant at 
1%. Each regression additionally contains dummies indicating tube well non-availability in school and at home, 
whether tube well at school is arsenic-contaminated and a set of 5 dummies indicating which day of the week 
the test was taken. All specifications control for regional FE. Specification (5) additionally instruments the 
school type (whether an Islamic school). 
 
 
  Lastly, a potential concern of our identification strategy is that the incidence of 
arsenicosis may be localized – even within the same administrative region (i.e. union), some 
cluster of households could be more affected by arsenic contamination. If so, this would 
lead to violation of the exclusion restriction. To this end, we estimate the educational 
production function restricting our sample to children who are not affected by arsenicosis
10. 
And because assignment to arsenic-contaminated water well is random, we use the resultant 
exogenous variation in student achievement to identify peer effects on the test score of 
                                                 
10 This stratification strategy is similar to Bobonis and Finan (2007) who use the exogenous variation in school 
participation (caused by a randomly placed program, namely the Progresa program) to identify peer effects on 
the school enrolment of ineligible children residing in the same communities. 
  5unaffected children residing in the same communities. We find that peers have considerable 
influence on the enrollment decision of children from arsenic-free households.  
 
 
Table 2: OLS and 2SLS estimates of peer effects, sample of arsenic-free children 
 
 (1) (2) (3) 
  OLS 2SLS 1st stage 2SLS  1st stage
Mean maths score of peers  0.960 0.680 0.604 
 (78.65)** (1.87)+ (1.62) 
Fraction of peers with arsenic-affected 
homes tubewells  -0.047  -0.044
 (2.94)**   (2.79)**
N 6785 5671 5671 5671  5671
Control for family and school attributes?  Yes Yes Yes Yes  Yes
Regional FEs?  Yes Yes Yes Yes  Yes
F-test   8.66 7.80 
Overid --- 0.13 
R-squared 0.51 0.45 0.07 0.43  0.07
Notes: Sample as Table 1. 
 
To conclude, the evidence of endogenous social effect has important implications 
for policy. An endogenous effect is characterized by a multiplier effect: government 
interventions to boost the learning of one child raises the schooling of other children in the 
reference population which in turn further boosts the schooling of the targeted child, 
therefore resulting in large social multiplier effects. 
 
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Social interactions and student achievement in a developing country : An instrumental variables approach

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Social interactions and student achievement in a developing country : An instrumental variables approach

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