Design of Randomized Experiments to Measure Social Interaction
Effects
Jinyong Hahn
UCLA
*
Keisuke Hirano
University of Arizona
†
27 January 2009
Abstract
We consider the use of randomized experiments to measure social interaction effects. Ran
domization at two levels—across groups and within groups—can resolve an omitted variables
problem for a linearinmeans model of endogenous social interactions.
We examine how the
randomization should be carried out to estimate the coefficients of interest most precisely, and
calculate the optimal treatment probabilities under different criteria.
1
Introduction
There has been considerable work in recent years on estimating models where individuals within a
group influence each other’s behavior. Brock and Durlauf (2001) and Moffitt (2001) survey recent
studies of social interaction effects.
Models with social interaction effects present severe identification problems, as was pointed out
in the seminal paper by Manski (1993). We consider a version of Manski’s linearinmeans model
of social interactions, and show how a randomization can be used to identify the model. Then we
consider the experimental design issue: how should the randomization probabilities be chosen to
obtain the most precise estimates of the coefficients of interest? We calculate the optimal treatment
probabilities under certain criteria. We find that for some criteria, the design used by Duflo and
Saez (2003) is nearly optimal.
*
Department of Economics, University of California, Los Angeles, Box 951477, Los Angeles, CA 900951477
([email protected])
†
Department of Economics, University of Arizona, Tucson, AZ 85721 ([email protected])
1
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2
LinearinMeans Model
Suppose we observe
N
nonoverlapping groups
g
= 1
, . . . , N
.
For each group
g
, we sample
M
g
individuals. We assume that the
M
g
individuals form a random subset of the full group, and we
assume that all the variables of interest are independent across groups.
Consider the following linearinmeans model of social interactions, which is a special case of
the model introduced by Manski (1993):
y
gi
=
E
g
[
y
gi
]
β
+
x
gi
η
+
α
gi
+
gi
,
(1)
where all variables are measured in deviations from sample means, and
E
g
[
·
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 Fall '08
 Staff
 Sociology, The Land, Randomness, LGI, Social interaction effects, Manski

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