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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
Charles F. Manski
To cite this article: Charles F. Manski (2013) Comment, Journal of Business & Economic
Statistics, 31:3, 273-275, DOI: 10.1080/07350015.2013.792262
To link to this article: http://dx.doi.org/10.1080/07350015.2013.792262
Published online: 22 Jul 2013.
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Manski: Comment 273
strategic network formation are still in their infancy (Christakis et al.2010; Mele2011; Chandrasekhar and Jackson2012; Leung 2013). The very important lesson that we should take from the analysis of Goldsmith-Pinkham and Imbens is that accounting for the endogeneity of relationships in analyses of peer effects is feasible, and can provide substantial new insights, for example, into unobserved characteristics that might correlate both with behavior and friendship formation. The specifications that are needed to properly model both network formation and peer ef-fects require careful additional analysis in context, and provide us with a rich agenda going forward.
REFERENCES
Aral, S., Muchnik, L., and Sundararajan, A. (2009), “Distinguishing Influ-ence Based Contagions from Homophily Driven Diffusion in Dynamic Net-works,”Proc. Natl. Acad. Sci., 106, 21544–21549. [270]
Bala, V., and Goyal, S. (2000), “A Noncooperative Model of Network Forma-tion,”Econometrica, 68, 1181–1229. [272]
Banerjee, A., Chandrasekhar, A., Duflo, E., and Jackson, M. (2012), “Dif-fusion of Microfinance,” NBER Working Paper 17743. Available at http://www.stanford.edu/jacksonm/diffusionofmf.pdf. [272]
Blume, L., Brock, W., Durlauf, S., and Ioannides, Y. (2011), “Identification of Social Interactions,” inThe Handbook of Social Economics, ed. J. Benhabib, A. Bisin, and M. Jackson, San Diego: North Holland. [270]
Bramoull´e, Y., Djebbari, H., and Fortin, B. (2009), “Identification of Peer Effects Through Social Networks,”Journal of Econometrics, 150, 41–55. [270]
Centola, D. (2010), “The Spread of Behavior in an Online Social Network Experiment,”Science, 32, 1194–1197, doi: 10.1126/science.1185231. [270] Chandrasekhar, A., and Jackson, M. (2012), “Tractable and Consis-tent Random Graph Models,” SSRN Working Paper. Available at
http://ssrn.com/abstract=2150428. [270,273]
Christakis, N., Fowler, J., Imbens, G., and Kalyanaraman, K. (2010), “An Em-pirical Model for Strategic Network Formation,” NBER Working Paper. [273]
Currarini, S., Jackson, M., and Pin, P. (2009), “An Economic Model of Friend-ship: Homophily, Minorities, and Segregation,”Econometrica, 77, 1003– 1045. [271]
Currarini, S., Jackson, M., and Pin, P. (2010), “Identifying the Roles of Race-Based Choice and Chance in High School Friendship Network Formation,”
Proceedings of the National Academy of Sciences, 107, 4857–4861. [271] Duflo, E., and Saez, E. (2003), “The Role of Information and Social Interactions
in Retirement Plan Decisions: Evidence From a Randomized Experiment,”
Quarterly Journal of Economics, 118, 815–842. [270]
Goldsmith-Pinkham, P., and Imbens, G. (2013), “Social Networks and the Iden-tification of Peer Effects,”Journal of Business and Economic Statistics, 31, 253–264. [271]
Jackson, M. (2008),Social and Economic Networks, Princeton, NJ: Princeton University Press. [270,272]
Jackson, M., Barraquer, T., and Tan, X. (2012), “Social Capital and Social Quilts: Network Patterns of Favor Exchange,”American Economic Review, 102, 1857–1897. [272]
Jackson, M., and Wolinsky, A. (1996), “A Strategic Model of Social and Eco-nomic Networks,”Journal of Economic Theory, 71, 44–74. [272] Leung, M. (2013), “Two-Step Estimation of Network-Formation Models With
Incomplete Information,” Working Paper, Stanford University. [273] Manski, C. (1993), “Identification of Endogenous Social Effects: The Reflection
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Mele, A. (2011). “A Structural Model of Segregation in Social Networks,” Working Paper, Johns Hopkins University. [273]
Comment
Charles F. M
ANSKIDepartment of Economics and Institute for Policy Research, Northwestern University, Evanston, IL 60201 ([email protected])
To begin, I will express mixed feelings about the decision by Goldsmith-Pinkham and Imbens to attach my name to the linear-in-means models that are the concern of their article. I will not object strenuously to their invention of the acronym MLIM model, if only because I am aware of the adage that “any publicity is good publicity, as long as they spell your name right.” However, I will note that Manski (1993) did not origi-nate linear-in-means models, whose use in empirical research goes back at least to the 1960s and perhaps earlier. Nor did my article advocate empirical application of these models to study social interactions—it also studied nonparametric models and parametric nonlinear ones, taking no position on the realism of any of them. My objective in writing the article was to an-alyze identification of models with endogenous social effects, recognizing that the outcomes in such models solve equilibrium conditions. For this purpose, linear-in-means models provided an analytically tractable case that illustrates well some basic issues.
I similarly interpret Goldsmith-Pinkham and Imbens not to be advocating linear-in-means models but rather to be focus-ing on these models to illustrate some basic issues. Their article extends the literature in several directions. One that I find partic-ularly interesting is their development of some relatively simple
economic models of network formation and integration of these models with study of interactions within the formed networks. Another is their use of Bayesian inferential methods to circum-vent conceptually and technically difficult issues that arise in performing frequentist inference in settings where a population does not partition into a large set of separate networks. When making these contributions, the authors maintain parametric modeling assumptions that may be too restrictive to provide a realistic basis for credible empirical analysis. Yet, as with the linear-in-means model itself, I can appreciate the illustrative value of focusing attention on tractable special cases.
SPECIFYING THE OBJECT OF INTEREST
I will focus my comment on one passage in the article by Goldsmith-Pinkham and Imbens, where they consider the object of interest for empirical analysis of social interactions. They write
© 2013American Statistical Association Journal of Business & Economic Statistics July 2013, Vol. 31, No. 3
DOI:10.1080/07350015.2013.792262
274 Journal of Business & Economic Statistics, July 2013
The main object of interest is the effect of peers’ outcomes on own outcomes. . . .Also of interest is the exogenous peer effect. . . .
Here we interpret the endogenous effect as the average change we would see in an individual’s outcome if we changed their peer’s outcomes directly. . . In some cases this may be difficult to envision. In our example, we will think of this as something along the lines of the direct, causal, effect of providing special tutoring to one’s peers on one’s own outcome. . . . .The exogenous effect is interpreted as the causal effect of changing the peer’s covariate values. For some covariates, this thought experiment may be difficult, but for others, especially lagged values of choices, it may be feasible to consider interventions that would change those values for the peers.
It is accurate that the extant literature has taken the main object of interest to be the endogenous effect, with secondary interest in the exogenous effect. However, my own thinking on this matter has evolved over the past 20 years. Whereas Manski (1993) focused primarily on the endogenous effect, I have long been concerned that this rarely is the object of interest from the perspective of policy formation. The reason is that a policy maker can rarely manipulate peer outcomes directly. Moreover, if a policy maker somehow is able to manipulate peer outcomes, then doing so breaks the equilibrium conditions of endogenous effects models.
Motivated by policy concerns, Manski (2013) studied settings with endogenous effects as problems of analysis of treatment response with social interactions. The treatments are variables that a policy maker can manipulate, which may jointly affect the outcomes of all persons in a network. An endogenous effects model specifies a mechanism through which treatment response may propagate through the network.
The analysis in the published version of Manski (2013) is entirely nonparametric, but earlier working paper versions used a linear-in-means model to illustrate abstract ideas. Writing a comment on the article by Goldsmith-Pinkham and Imbens pro-vides me with an opportunity to place this illustration in print.
ANALYSIS OF TREATMENT RESPONSE IN A LINEAR-IN-MEANS MODEL
Here is the basic setup considered in Manski (2013). Let Jbe a population and (J,,P) be a probability space. LetTbe a set of feasible treatments and letTJ≡ ×
j∈JT be the space of
treatment vectors potentially assigned to the entire population. For eachj∈J, let response functionyj(·):TJ→Y map treatment
vectors into potential outcomes. Thus,yj(tJ) is the outcome for
j under a specified treatment vectortJ≡(t
k,k ∈J). Personj
has realized treatmentzj and outcomeyj≡yj(zJ). Observation
of [(yj,zj),j∈J] revealsP(y,z), henceP[y(zJ)]. The objective is
to learn the distribution of treatment response undertJ, that is,
P[y(tJ)].
A simple linear-in-means model emerges if the population partitions into symmetric reference groups characterized by val-ues for an observed covariatex. Each group contains a contin-uum of persons. The linear-in-means model assumes that for each personj
yj(tJ)=α+β1tj +β2E(t|xj)+γ E[y(tJ)|xj]+uj. (1)
Here, parameterβ2 measures the exogenous effect andγ the
endogenous effect. Taking expectations conditional onxjyields
E[y(tJ)|xj]=α+(β1+β2)E(t|xj)+γ E[y(tJ)|xj] Insertion of the right-hand side of Equation (3) into the struc-tural function (1) yields the response function
yj(tj)= Thus, the response function is the reduced form of the struc-tural function.
The model thus far does not pin down the structural or re-sponse functions. The reason is that it does not restrict the un-observed covariates (uj,j∈J). Assume thatE(u|z, x)=0. This
implies a linear mean regression relating realized treatments and outcomes:
Observation of realized treatments and outcomes reveals E(y|z, x) on the support of (z,x). Hence,ϕ is point-identified if the support of [1,z,E(z|x)] is not contained in a linear sub-space ofR3. Knowledge ofϕand the empirical evidence imply
knowledge of (uj,j∈J). Finally, knowledge ofϕand (uj,j∈J)
implies knowledge of the response functions [yj(·),j∈J].
Note that point-identification of the response-function pa-rametersϕ does not imply point-identification of the structural parameters (α,β1,β2,γ).β1 is point-identified but (α,β2,γ)
are not. Thus, one cannot distinguish exogenous from endoge-nous effects under the maintained assumptions. Nevertheless, the assumptions fully reveal the population vector of response functions.
WHEN IS IT IMPORTANT TO IDENTIFY THE STRUCTURAL PARAMETERS?
The above shows that point-identification of the structural parameters is not a prerequisite for point-identification of treat-ment response. Yet inference on structural parameters has been the dominant theme of modern econometric analysis of social interactions. It also has been the dominant theme of the classi-cal literature on identification of linear simultaneous equations. A rare exception was voiced by Arthur Goldberger in hisET Interview. Responding to a question from Nick Kiefer, Gold-berger said (Kiefer and GoldGold-berger1989, p. 150): “Well, that’s one position, that the entire content in a structural model is simply in the restrictions, if any, that it implies on the reduced form—that’s true. That gives priority to the reduced form.”
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)=
α
1−γ +β1tj +
γ β1+β2
1−γ E(t|x)+uj
+ϕ0+ϕ1tj +ϕ2E(t|xj)+uj. (6)
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 ([email protected])
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
