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From Natural Variation to Optimal Policy? The Importance of Endogenous Peer Group Formation
 Econometrica
, 2013
"... We take cohorts of entering freshmen at the United States Air Force Academy and assign half to peer groups designed to maximize the academic performance of the lowest ability students. Our assignment algorithm uses nonlinear peer effects estimates from the historical pretreatment data, in which st ..."
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Cited by 29 (1 self)
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We take cohorts of entering freshmen at the United States Air Force Academy and assign half to peer groups designed to maximize the academic performance of the lowest ability students. Our assignment algorithm uses nonlinear peer effects estimates from the historical pretreatment data, in which students were randomly assigned to peer groups. We find a negative and significant treatment effect for the students we intended to help. We provide evidence that within our "optimally" designed peer groups, students avoided the peers with whom we intended them to interact and instead formed more homogeneous subgroups. These results illustrate how policies that manipulate peer groups for a desired social outcome can be confounded by changes in the endogenous patterns of social interactions within the group. KEYWORDS: Peer effects, social network formation, homophily. INTRODUCTION PEER EFFECTS HAVE BEEN widely studied in the economics literature due to the perceived importance peers play in workplace, educational, and behavioral outcomes. Previous studies in the economics literature have focused almost exclusively on the identification of peer effects and have only hinted at the potential policy implications of the results. 2 Recent econometric studies on assortative matching by 3 This study takes a first step in determining whether student academic performance can be improved through the systematic sorting of students into peer groups. We first identify nonlinear peer effects at the United States Air Force Academy (USAFA) using pretreatment data in which students were randomly assigned to peer groups (squadrons) of about 30 students. These estimates showed that low ability students benefited significantly from being with peers who have high SAT Verbal scores. We use these estimates to create optimally designed peer groups intended to improve academic achievement of the 1 This article was completed under a Cooperative Research and Development Agreement with the U.S. Air Force Academy. This research was partially funded by the National Academy of Education, the National Science Foundation, and Spencer Foundation. Thanks to D. Staiger, R. Fullerton, R. Schreiner, B. Bremer, K. SilzCarson, and K. Calahan. 2 For recent studies in higher education, see 3 Unless the peer effects include a nonlinearity, there is no social gain to sorting individuals into peer groups. With a linear in means effect, a "good" peer taken from one group and placed into another group will have equal and offsetting effects on both groups. See Bénabou (1996) for a discussion of how moments other than the mean may be critical to determining outcomes.
2009b), “Beware of Economists Bearing the Reduced Forms? An Experiment in How Not To Improve Student Outcomes,” mimeo UCDavis
"... We begin with peer effects estimates from randomly assigned peer groups at the United States Air Force Academy. We then take subsequent cohorts of entering freshmen and assign half of the students to peer groups (squadrons) in a way intended to maximize the academic performance of students with the ..."
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Cited by 11 (0 self)
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We begin with peer effects estimates from randomly assigned peer groups at the United States Air Force Academy. We then take subsequent cohorts of entering freshmen and assign half of the students to peer groups (squadrons) in a way intended to maximize the academic performance of students with the lowest incoming ability. We find a negative and statistically significant treatment effect for the students we intended to help. We explore three possible explanations for this perverse finding including the hypothesis (which we can reject) that the original findings were spurious. We show that our “optimal ” assignment mechanism created bifurcated squadrons that had a social dynamic entirely different from most squadrons seen in the observational data. Our results suggest that even in a well understood and self contained environment, using reducedform estimates to make outofsample policy predictions can lead to unanticipated and potentially negative consequences. 1
Inferring Welfare Maximizing Treatment Assignment under Budget Constraints. NBER Working Paper No
, 2008
"... This paper concerns the problem of allocating a binary treatment among a target population based on discrete and continuous observed covariates. The goal is to maximize the mean social utlity of an eventual outcome when a budget constraint limits what fraction of the population can be treated. We pr ..."
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Cited by 7 (0 self)
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This paper concerns the problem of allocating a binary treatment among a target population based on discrete and continuous observed covariates. The goal is to maximize the mean social utlity of an eventual outcome when a budget constraint limits what fraction of the population can be treated. We propose a treatment allocation procedure based on sample data from randomized treatment assignment. We examine this procedure in the light of statistical decision theory and derive asymptotic frequentist properties of the allocation rule and the welfare generated from it. The resulting distribution theory is used to conduct inference on the welfare loss resulting from restricted covariate choice and on the dual value, i.e. the minimum resources needed to attain aspecific average welfare via efficient treatment assignment. The methodology is applied to the optimal provision of antimalaria bed net subsidies, using data from a randomized experiment conducted in western Kenya. We find that a government which can afford to distribute bed net subsidies to only 50 % of its target population can, with an efficient allocation rule based on multiple covariates, increase bednet use by 8 percentage points (25 percent) relative to random allocation and by 4 percentage points (11 percent) relative to one based on wealth only. Our methods do not rely on functional form assumptions and can be extended to situations encompassing conditional cash transfers, imperfect treatment takeup and spillover effects on noneligibles. 1
From Natural Variation to Optimal Policy: A Cautionary Tale in How Not to Improve Student Outcomes," Manuscript
, 2010
"... We begin with peer effects estimates from randomly assigned peer groups at the United States Air Force Academy. We then take subsequent cohorts of entering freshmen and assign half of the students to peer groups (squadrons) in a way intended to maximize the academic performance of students with the ..."
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Cited by 4 (0 self)
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We begin with peer effects estimates from randomly assigned peer groups at the United States Air Force Academy. We then take subsequent cohorts of entering freshmen and assign half of the students to peer groups (squadrons) in a way intended to maximize the academic performance of students with the lowest incoming ability. We find a negative and statistically significant treatment effect for the students we intended to help. We explore three possible explanations for this perverse finding including the hypothesis (which we can reject) that the original findings were spurious. We show that our “optimal ” assignment mechanism created bifurcated squadrons that had a social dynamic entirely different from most squadrons seen in the observational data. Our results suggest that even in a well understood and self contained environment, using reducedform estimates to make outofsample policy predictions can lead to unanticipated and potentially negative consequences. 1
Inferring optimal resource allocations from experimental data,”Journal of the American Statistical Association, forthcoming
, 2008
"... This paper concerns the problem of optimally allocating a scarce indivisible resource among a target population based on experimental data for a sample drawn from this population. For a wide class of social welfare functions, the problem can be set up as a mathematical program with estimated compone ..."
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This paper concerns the problem of optimally allocating a scarce indivisible resource among a target population based on experimental data for a sample drawn from this population. For a wide class of social welfare functions, the problem can be set up as a mathematical program with estimated components. The paper provides a framework for statistical inference on the estimated optimal solutions and corresponding optimal values. The analysis carefully distinguishes between situations of uniqueness, nonuniqueness and near nonuniqueness of the solutions and shows that in the nearly nonunique case, subsampling gives inconsistent inference. Yet, confidence intervals which are potentially conservative but robust to the degree of uniqueness can be constructed. A key contribution of this paper is to show that applicability of these techniques extends beyond linear maximands like the mean
Diversity is the Optimal Education Strategy: A Mathematical Proof”,
 International Journal of Innovative Management, Information & Production (IJIMIP),
, 2013
"... Abstract To enhance learning, it is desirable to also let students learn from each other, e.g., by working in groups. It is known that such groupwork can improve learning, but the effect strongly depends on how we divide students into groups. In this paper, we describe how to optimally divide stude ..."
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Abstract To enhance learning, it is desirable to also let students learn from each other, e.g., by working in groups. It is known that such groupwork can improve learning, but the effect strongly depends on how we divide students into groups. In this paper, we describe how to optimally divide students into groups so as to optimize the resulting learning. It turns out that the largest gain is attained when each of the resulting groups is a representative sample for the student population as a whole i.e., when we have diversity.
How to Divide Students into Groups so as to Optimize Learning: Towards a Solution to a PedagogyRelated Optimization Problem
"... Abstract—To enhance learning, it is desirable to also let students learn from each other, e.g., by working in groups. It is known that such groupwork can improve learning, but the effect strongly depends on how we divide students into groups. In this paper, based on a first approximation model of st ..."
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Abstract—To enhance learning, it is desirable to also let students learn from each other, e.g., by working in groups. It is known that such groupwork can improve learning, but the effect strongly depends on how we divide students into groups. In this paper, based on a first approximation model of student interaction, we describe how to optimally divide students into groups so as to optimize the resulting learning. We hope that, by taking into account other aspects of student interaction, it will be possible to transform our solution into truly optimal practical recommendations. Index Terms—optimization, groupwork, uncertainty I.
credit, including © notice, is given to the source. From Natural Variation to Optimal Policy? The Lucas Critique Meets Peer Effects
, 2011
"... JEL No. I2,J01 We take cohorts of entering freshmen at the United States Air Force Academy and assign half to peer groups with the goal of maximizing the academic performance of the lowest ability students. Our assignment algorithm uses peer effects estimates from the observational data. We find a n ..."
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JEL No. I2,J01 We take cohorts of entering freshmen at the United States Air Force Academy and assign half to peer groups with the goal of maximizing the academic performance of the lowest ability students. Our assignment algorithm uses peer effects estimates from the observational data. We find a negative and significant treatment effect for the students we intended to help. We show that within our “optimal ” peer groups, students selfselected into bifurcated subgroups with social dynamics entirely different from those in the observational data. Our results suggest that using reducedform estimates to make outofsample