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Journal of Business & Economic Statistics
ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20
Comment
Bruce Sacerdote
To cite this article: Bruce Sacerdote (2013) Comment, Journal of Business & Economic Statistics, 31:3, 275-275, DOI: 10.1080/07350015.2013.792263
To link to this article: http://dx.doi.org/10.1080/07350015.2013.792263
Published online: 22 Jul 2013.
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Sacerdote: Comment 275
One reason for inference on structural parameters may be “science.” Researchers may want to characterize reality, as an end in itself. A different reason is to predict treatment response when aregime change(anuber treatment) alters part of a struc-tural model in a known way, leaving other parts invariant. Then response functions change in a way that can be predicted with knowledge of the structural model but not otherwise.
Consider the linear-in-means response function
yj(tJ)=
A regime change might alter some of the structural parameters (α,β1,β2,γ) in a known way while leaving others unchanged. Then knowledge of (α,β1,β2,γ) enables prediction of treatment response but knowledge of (ϕ0,ϕ1,ϕ2) does not.
REFERENCES
Kiefer, N., and Goldberger, A. (1989), “The ET Interview: Arthur S. Goldberger,”Econometric Theory, 5, 133–160. [274]
Manski, C. (1993), “Identification of Endogenous Social Effects: The Reflection Problem,”Review of Economic Studies, 60, 531–542. [273,274]
—— (2013), “Identification of Treatment Response with Social Interactions,” The Econometric Journal, 16, S1–S23. [274]
Comment
Bruce S
ACERDOTEDepartment of Economics, Dartmouth College, Hanover, NH 03755 and NBER (Bruce.Sacerdote@dartmouth.edu)
This is an innovative article and a nice addition to the lit-erature on the estimation of endogenous and exogenous peer effects. There are two main contributions. First, the authors suggest that we can incorporate the endogeneity of peer choice in a parsimonious way. The authors introduce an unobserved individual specific parameterξi. For any two individualsiand
j, the distance betweenξi andξj affects the probability thati
andjform a link. Then thisξiis introduced directly and linearly
(in Equation (6.1)) as a determinant ofi’s outcomeYi. This is a
very clever approach and has the potential to greatly reduce the complexity of an otherwise intractable problem.
The second advance of the article is to show that all the model’s parameters (including theξi’s) can in principle be
es-timated in a Bayesian framework using Monte Carlo methods. This answers the obvious question of how we might estimate the individual specific unobserved regressor.
The authors proceed to estimate their model using Ad Health data and calculating exogenous and endogenous peer effects on own Grade Point Average. The estimates seem quite plausible. For example, an individual’s own past grades predict current grades with a coefficient of 0.73. Peers’ past grades predict own current grades with a coefficient of 0.11. Such estimates are in the same ballpark as existing articles that have random assignment to classrooms.
Interestingly the introduction of endogenous network forma-tion (through the vector of etas) does not have a meaningful impact on the estimated peer effects. Compare, for example, the results in Tables 5 and 6, where the former table assumes that peer choice is exogenous. My own experimentation with the model found much the same result. Using data from a mil-itary academy with randomly assigned squadrons, I found that accounting for an individual specificξi (which affects friend
choice) affects the outcome, but does not affect the estimated peer effects. (My coauthors Scott Carrell and James West who have access to the data were kind enough to run the code for me.)
Besides being a fan of the article, I have two general com-ments. First, not all readers will accept the simple parameteri-zation of friendship choice as having solved the peer selection problem. I suspect that the authors’ formulation works particu-larly well in their example and in my example because in both cases we have strong controls for own ability and peer (back-ground) ability. Staiger and Kane have convinced me that in test score value added models, having prior test scores does a great deal to compensate for the selection of students into classrooms and schools.
Second, economics researchers have become progressively less interested in the linear-in-means model. Models beyond the linear-in-means models allow the possibility for Pareto improv-ing reallocations of students, such as trackimprov-ing students (groupimprov-ing them into classrooms) by ability. Hoxby and Weingarth (2005) and my own work with Imberman and Kugler finds that non-linear models fit the data much better. I suspect that with a minimum of tinkering the authors’ model could be extended to a more flexible (nonlinear) formulation. Part of the beauty of the Markov chain Monte Carlo method being used is that a wide variety of models can be estimated even in cases where we cannot conduct maximum likelihood estimation.
Overall I found this to be a thoughtful article and a worthwhile contribution.
REFERENCE
Hoxby, C. M., and Weingarth, G. (2005), “Taking Race Out of the Equation: School Reassignment and the Structure of Peer Effects,” Working Paper, Harvard University. [275]
© 2013American Statistical Association
Journal of Business & Economic Statistics July 2013, Vol. 31, No. 3 DOI:10.1080/07350015.2013.792263
