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Journal of Business & Economic Statistics
ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20
Rejoinder
Paul Goldsmith-Pinkham & Guido Imbens
To cite this article: Paul Goldsmith-Pinkham & Guido Imbens (2013) Rejoinder, Journal of Business & Economic Statistics, 31:3, 279-281, DOI: 10.1080/07350015.2013.792260
To link to this article: http://dx.doi.org/10.1080/07350015.2013.792260
Published online: 22 Jul 2013.
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Goldsmith-Pinkham and Imbens: Rejoinder 279
Goldberger, A. (1991),A Course in Econometrics, Cambridge, MA: Harvard University Press. [277]
Goldsmith-Pinkham, P., and Imbens, G. W. (2013), “Social Networks and the Identification of Peer Effects,”Journal of Business and Economic Statistics, 31, 253–264. [276,278]
Graham, B. (2008), “Identifying Social Interactions Through Conditional Vari-ance Restrictions,”Econometrica, 76, 643–660. [276]
Graham, B., and Hahn, J. (2005), “Identification and Estimation of the Linear-in-Means Model of Social Interactions,”Economics Letters, 88, 1–6. [276]
Kline, B. (2012), “Identification of Complete Information Games,” Working Paper. [277]
Kline, B., and Tamer, E. (2012), “Bounds for Best Response Functions in Binary Games,”Journal of Econometrics, 166, 92–105. [277]
Lee, L. (2007), “Identification and Estimation of Econometric Models With Group Interactions, Contextual Factors and Fixed Effects,” Journal of Econometrics, 140, 333–374. [276]
Manski, C. (1993), “Identification of Endogenous Social Effects: The Reflection Problem,”Review of Economic Studies, 60, 531–542. [276]
Tamer, E. (2003), “Incomplete Simultaneous Discrete Response Model With Multiple Equilibria,” Review of Economic Studies, 70, 147– 165. [277]
Wooldridge, J. (2001),Econometric Analysis of Cross Section and Panel Data, Cambridge, MA: The MIT Press. [277]
Rejoinder
Paul G
OLDSMITH-P
INKHAMDepartment of Economics, Harvard University, Cambridge, MA 02138 (pgoldsm@fas.harvard.edu)
Guido I
MBENSGraduate School of Business, Stanford University, Stanford, CA 94305, and NBER (imbens@stanford.edu)
First of all, we thank the Coeditors again for inviting us to present the article and for organizing such a distinguished group of researchers to comment on our work. We would also like to thank these individuals for their thoughtful discussion. These comments contain a great number of interesting questions and suggestions for future research, more than we can hope to address in our response. This partly reflects the fertility of this area of study, and we hope and suspect that the comments will stimulate further research.
A general issue raised in three of the comments concerns the focus on model parameters versus specific policy interventions. Jackson stresses the importance of being very explicit about the specific effects of interest, while Manski takes issue with our claim that “the main object of interest is the effect of peers’ outcomes on own outcomes” and points out that identification of the structural parameters is not the same as identification of the treatment responses. Relatedly, Kline and Tamer raise the issue of the interpretation of the parameters and their link to policy interventions.
Here, we were less careful than we should have been. Ul-timately, we agree wholeheartedly with these comments and withdraw the claim to which Manski objects. Manski’s linear-in-means example illustrates nicely the pitfalls of focusing solely on identifying parameters rather than policies, and we believe this is an important issue. Too often econometricians focus solely on the particular parameters in their models without re-lating them to interpretable and feasible interventions. With this objective in mind, Kline and Tamer focus on the effect of a change in either one’s own or others’ covariate values on the out-come of interest. They demonstrate how these measured effects are related in potentially complicated ways to the parameters of the model.
In the area of industrial organization, it is often the norm to report the effects of specific counterfactuals or policy inter-ventions, while in other areas of empirical economic research, it is much less common. In peer effects models, there are
di-rect policy interventions to consider, but there are also other policies whose effects are complicated functions of the model parameters. For example, in the context of a network formation model, Christakis et al. (2010) considered the effect of chang-ing features of the assignment to classes on the formation of friendships. Given our setup, one could envision a policy af-fecting friendship formation that was enacted with students’ grades in mind. In sum, we agree with the recommendation that researchers should routinely assess the effects of specific and relevant interventions rather than simply report parameter estimates.
Kline and Tamer also study the interpretation of the model parameters themselves and show how they can be interpreted as “best responses” in a game. This greatly improves the inter-pretability of these parameters, although ultimately we would still stress the importance of focusing on the effect of interven-tions rather than the parameters themselves. In some cases, it seems likely that the peer effects model is attempting to capture the effects of a “social multiplier” through a specification that reflects the researcher’s ignorance about the particular chan-nels by which this interaction occurs. However, we agree with both Jackson and Sacerdote’s view that a researcher should be modeling the specific type of social interaction she hopes to find. Interestingly, as Manski points out in his comment and in Manski (2013), even researchers fortunate enough to have randomized interventions will have to think hard about how to model the social interaction.
Bramoull´e raises important issues regarding the type of en-dogeneity we allow for in our model, discusses some identifica-tion quesidentifica-tions, and offers some suggesidentifica-tions on estimaidentifica-tion and on modeling heterogeneity in peer effects. It is interesting as a
© 2013American Statistical Association Journal of Business & Economic Statistics
July 2013, Vol. 31, No. 3 DOI:10.1080/07350015.2013.792260
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general matter that the econometrics literature lumps together various sources of endogeneity without a well-established termi-nology to distinguish between them. In our model, we introduce into the network literature a form of “omitted-variable endo-geneity,” as opposed to “simultaneous equations endogeneity.” If we were to observe theξi that are unobserved in our model, the endogeneity we are concerned with would disappear.
A very different, and arguably more challenging, form of endogeneity would arise if decisions concerning the formation of links and outcomes were taken simultaneously. The clear-est analog in the clear-established econometrics literature would be a nontriangular system of equations. What type of plausible in-formation and restrictions would allow researchers to establish the presence of that type of simultaneity is a very interesting and, at first sight, very difficult question that should be pursued in future research.
Bramoull´e also offers some comments on our Bayesian ap-proach. He suggests that advances in computational graph theory may facilitate the calculation of maximum likelihood estimators. This is an interesting suggestion, and there may well be compu-tational advantages to such an approach. However, our Bayesian approach was not solely motivated by computational reasons. It was also motivated by the lack of large sample results for maximum likelihood estimators in the current setting, whose difficulties are mentioned by Manski (which we will discuss shortly). If the suggestions regarding the computation of maxi-mum likelihood estimators would be effective, we would most certainly incorporate them in our computational algorithms but maintain the focus on posterior distributions rather than maxi-mum likelihood estimates.
Graham presents a very interesting set of new results, focus-ing on a novel problem where the unobserved components are analyzed as fixed effects rather than random effects. He studies a setting with observations on many small networks and derives novel identification results for such settings. In particular, he focuses on transitivity and state dependence in the dynamic paths of the network. Using an example with observations on many networks with three individuals, followed for three periods, he shows how the presence of state dependence (where having a link between two individuals in the current period affects the changes of the link in the next period, similar to our
D0,ij), and transitivity (where links between two individuals are more likely if they had friends in common in the previous period, an analog to our F0,ij) can be established under weak nonparametric conditions. This identification result, and the generalization to the case with larger networks, is a very interesting finding and shows the scope for identification results that can genuinely improve our understanding of what can be learned from observations on networks.
More generally, identification is a difficult issue in network settings. In conventional cross-section settings, identification questions are often formulated as the ability to infer the pa-rameters of interest from the joint distribution of some vari-ables (Y, X). The hope is that, with sufficiently large samples, we can approximate this joint distribution accurately and if we can infer the parameters of interest from this distribution, we should be able to accurately estimate them as well. However, in the network setting, it is not clear what distribution we can
estimate in large samples. Clarification is needed in what de-fines a large sample and how the current sample differs from a larger sample. In Graham’s discussion, a larger sample is taken to mean more small networks are sampled; however, in many cases, this asymptotic approximation does not seem appropri-ate. Goldsmith-Pinkham and Imbens (2013) and Boucher and Mourifie (2012) made some progress toward furthering this re-search agenda, but much more is needed. We should note that related issues come up in the context of asymptotics in discrete choice models with large numbers of choices and large numbers of markets (Berry, Linton, and Pakes2004; Athey and Imbens 2007).
Sacerdote raises concerns with the linearity of the model. This is likely to be a very important issue in practice, as nonlinearity of the outcome equation in both covariates and peer effects can generate complex responses to policy interventions. It is a challenge, however, to introduce such nonlinear effects in a flexible and yet parsimonious manner. For example, simply allowing the effects of the own covariates to be nonlinear would be straightforward, but allowing the exogenous and endogenous peer effects to be nonlinear may lead to concerns regarding the identification of the models. These are clearly issues that need to be investigated further. The type of experimental data from the Air Force Academy that Sacerdote has studied (Carell, Sacerdote, and West2013) may be useful to this end.
Jackson outlines the broad set of econometric issues that applied researchers studying peer effects face, including identi-fication, the distinction between endogeneity and homophily in unobserved characteristics, computational challenges, measure-ment error in links, and misspecification, specifically that of the relevant set of peers. He also warns against the temptation to focus on simple models as suitable for many different settings. We agree with these concerns and the research agenda implictly laid out.
Another issue raised by Jackson concerns the potential in-adequacy of the two-mass-point distribution of the unobserved component of the individual characteristics. We agree that the assumption of two mass points is limiting, although in other areas, such as the literature on duration models, approximations based on simple discrete distributions have been found to be fairly accurate in simulations. More research is needed here to assess the restrictiveness of such distributional assumptions.
We see the area of peer effects, especially in settings where the peer groups are not obviously exogenous, as one with great challenges, and, as a result, as a very fertile one for new research. We recognize as well that our article raises more questions than it answers. As a general matter, it appears clear to us that there will not be simple solutions to each of these problems, and there will not be a simple model that can incorporate all these concerns.
Nevertheless, there are many areas where much progress can be made. We see the role of econometricians in this area primar-ily as one of developing models that address the complications listed by Jackson. A key concern in addressing these problems is maintaining tractability. Jackson, here and in other work, has stressed the severe computational difficulties facing researchers attempting to address the econometric issues. We feel that an important contribution of our current article is the multiple
Goldsmith-Pinkham and Imbens: Rejoinder 281
networks approach with the peer effects from two or more net-works as in Equation (7.1). Such multiple network models are natural generalizations of single network models that maintain tractability but allow researchers to investigate a range of issues related to endogeneity of networks, measurement error in links, and heterogeneity in peer effects. These models also begin to connect the peer effects models with spatial dependence mod-els more generally, allowing more flexible forms of dependence than the simple models with equal effects from all peers.
Additionally, we feel that econometricians must push to in-corporate better datasets of networks and peer interaction. Gra-ham’s results are an excellent example of how econometricians can help to guide applied researchers in their collection of new network data connected with outcomes. Larger and more robust datasets will allow researchers to answer the research questions regarding nonlinearities and nonparametric identification raised by the comments.
ADDITIONAL REFERENCES
Athey, S., and Imbens, G. (2007), “Discrete Choice Models With Multiple Unobserved Characteristics,”International Economic Review, 48, 1159– 1192. [280]
Berry, S., Linton, O., and Pakes, A. (2004), “Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems,”Review of Eco-nomic Studies, 71, 613–654. [280]
Boucher, V., and Mourifie, I. (2012), “My Friend Far Far Away: Asymp-totic Properties of Pairwise Stable Networks,” Working Paper. Available athttp://ssrn.com/abstract=2170803. [280]
Carrell, S. E., Sacerdote, B. I., and West, J. E. (2013), “From Natural Variation to Optimal Policy? The Importance of Endogenous Peer Group Formation,” Econometrica, 81, 855–882. [280]
Christakis, N. A., Imbens, G. W., Fowler, J. H., and Kalyanaraman, K. (2010), “An Empirical Model for Strategic Network Formation,” NBER Working Paper no. w16039, Cambridge, MA. [279]
Goldsmith-Pinkham, and Imbens. (2013), “Large-Sample Asymptotics for Net-work Statistics,” Working Paper, Harvard University. [280]
Manski, C. F. (2013), “Identification of Treatment Response With Social In-teractions,”The Econometrics Journal, 16, S1–S23. doi: 10.1111/j.1368-423X.2012.00368.x. [279]
