Email eric.auerbach [at] northwestern.edu
Phone (847) 491-4416
Address Northwestern University Department of Economics 2211 Campus Drive Evanston, IL 60208
I am an Assistant Professor in the Department of Economics at Northwestern University.
My research interests are in Econometrics and Network Economics.
CV
My research interests are in Econometrics and Network Economics.
CV
Publications
"Identification and Estimation of a Partially Linear Regression Model using Network Data" [arXiv]
Econometrica 90.1 (2022): 347-365
I study a regression model in which one covariate is an unknown function of a latent driver of link formation in a network. Rather than specify and fit a parametric network formation model, I introduce a new method based on matching pairs of agents with similar columns of the squared adjacency matrix, the ijth entry of which contains the number of other agents linked to both agents i and j. The intuition behind this approach is that for a large class of network formation models the columns of this matrix characterize all of the identifiable information about individual linking behavior. In the paper, I first describe the model and formalize this intuition. I then introduce consistent estimators for the parameters of the regression model.
"Testing for Differences in Stochastic Network Structure" [online appendix, arXiv]
Example R code [another link]
Econometrica 90.3 (2022): 1205–1223
How can one determine whether a community-level treatment, such as the introduction of a social program or trade shock, alters agents' incentives to form links in a network? This paper proposes analogues of a two-sample Kolmogorov-Smirnov test, widely used in the literature to test the null hypothesis of "no treatment effects," for network data. It first specifies a testing problem in which the null hypothesis is that two networks are drawn from the same random graph model. It then describes two randomization tests based on the magnitude of the difference between the networks' adjacency matrices as measured by the 2→2 and ∞ →1 operator norms. Power properties of the tests are examined analytically, in simulation, and through two real-world applications. A key finding is that the test based on the ∞ →1 norm can be substantially more powerful than that based on the 2→2 norm for the kinds of sparse and degree-heterogeneous networks common in economics.
"Exposure Effects are Not Automatically Useful for Policymaking" [online appendix, arXiv] (with Jonathan Auerbach and Max Tabord-Meehan)
Biometrika 111.1 (2024): 21–24Invited Discussion Paper
We thank Savje (2023) for a thought-provoking article and appreciate the opportunity to share our perspective as social scientists. In his article, Savje recommends misspecified exposure effects as a way to avoid strong assumptions about interference when analyzing the results of an experiment. In this discussion, we highlight a key limitation of Savje’s recommendation. Exposure effects are not generally useful for evaluating social policies without the strong assumptions that Savje seeks to avoid.
"Identification and Estimation of a Partially Linear Regression Model using Network Data" [arXiv]
Econometrica 90.1 (2022): 347-365
I study a regression model in which one covariate is an unknown function of a latent driver of link formation in a network. Rather than specify and fit a parametric network formation model, I introduce a new method based on matching pairs of agents with similar columns of the squared adjacency matrix, the ijth entry of which contains the number of other agents linked to both agents i and j. The intuition behind this approach is that for a large class of network formation models the columns of this matrix characterize all of the identifiable information about individual linking behavior. In the paper, I first describe the model and formalize this intuition. I then introduce consistent estimators for the parameters of the regression model.
"Testing for Differences in Stochastic Network Structure" [online appendix, arXiv]
Example R code [another link]
Econometrica 90.3 (2022): 1205–1223
How can one determine whether a community-level treatment, such as the introduction of a social program or trade shock, alters agents' incentives to form links in a network? This paper proposes analogues of a two-sample Kolmogorov-Smirnov test, widely used in the literature to test the null hypothesis of "no treatment effects," for network data. It first specifies a testing problem in which the null hypothesis is that two networks are drawn from the same random graph model. It then describes two randomization tests based on the magnitude of the difference between the networks' adjacency matrices as measured by the 2→2 and ∞ →1 operator norms. Power properties of the tests are examined analytically, in simulation, and through two real-world applications. A key finding is that the test based on the ∞ →1 norm can be substantially more powerful than that based on the 2→2 norm for the kinds of sparse and degree-heterogeneous networks common in economics.
"Exposure Effects are Not Automatically Useful for Policymaking" [online appendix, arXiv] (with Jonathan Auerbach and Max Tabord-Meehan)
Biometrika 111.1 (2024): 21–24Invited Discussion Paper
We thank Savje (2023) for a thought-provoking article and appreciate the opportunity to share our perspective as social scientists. In his article, Savje recommends misspecified exposure effects as a way to avoid strong assumptions about interference when analyzing the results of an experiment. In this discussion, we highlight a key limitation of Savje’s recommendation. Exposure effects are not generally useful for evaluating social policies without the strong assumptions that Savje seeks to avoid.
Working Papers
"Recovering Network Structure from Aggregated Relational Data using Penalized Regression" (with Hossein Alidaee and Michael P Leung)
Example R and Python code
Social network data can be expensive to collect. Breza et al. (2017) propose aggregated relational data (ARD) as a low-cost substitute that can be used to recover the structure of a latent social network when it is generated by a specific parametric random effects model. Our main observation is that many economic network formation models produce networks that are effectively low-rank. As a consequence, network recovery from ARD is generally possible without parametric assumptions using a nuclear-norm penalized regression. We demonstrate how to implement this method and provide finite-sample bounds on the mean squared error for the resulting estimator for the distribution of network links. Computation takes seconds for samples with hundreds of observations. Easy-to-use code in R and Python can be found here.
"The Local Approach to Causal Inference under Network Interference" (with Max Tabord-Meehan)
Revision requested at Quantitative Economics
We propose a new nonparametric modeling framework for causal inference when outcomes depend on how agents are linked in a social or economic network. Such network interference describes a large literature on treatment spillovers, social interactions, social learning, information diffusion, disease and financial contagion, social capital formation, and more. Our approach works by first characterizing how an agent is linked in the network using the configuration of other agents and connections nearby as measured by path distance. The impact of a policy or treatment assignment is then learned by pooling outcome data across similarly configured agents. We demonstrate the approach by proposing an asymptotically valid test for the hypothesis of policy irrelevance/no treatment effects and bounding the mean-squared error of a k-nearest- neighbor estimator for the average or distributional policy effect/treatment response.
"Identifying Socially Disruptive Policies" (with Yong Cai) [online appendix]
Example R code
Revision requested at The Review of Economic Studies
Social disruption occurs when a policy creates or destroys many network connections between agents. It is a costly side effect of many interventions and so a growing empirical literature recommends measuring and accounting for social disruption when evaluating the welfare impact of a policy. However, there is currently little work characterizing what can actually be learned about social disruption from data in practice. In this paper, we consider the problem of identifying social disruption in a research design that is popular in the literature. We provide two sets of identification results. First, we show that social disruption is not generally point identified, but informative bounds can be constructed using the eigenvalues of the network adjacency matrices observed by the researcher. Second, we show that point identification follows from a theoretically motivated monotonicity condition, and we derive a closed form representation. We apply our methods in two empirical illustrations and find large policy effects that otherwise might be missed by alternatives in the literature.
"Regression Discontinuity Design with Spillovers" (with Yong Cai and Ahnaf Rafi)
Researchers who estimate treatment effects using a regression discontinuity design (RDD) typically assume that there are no spillovers between the treated and control units. This may be unrealistic. We characterize the estimand of RDD in a setting where spillovers occur between units that are close in their values of the running variable. Under the assumption that spillovers are linear-in-means, we show that the estimand depends on the ratio of two terms: (1) the radius over which spillovers occur and (2) the choice of bandwidth used for the local linear regression. Specifically, RDD estimates direct treatment effect when radius is of larger order than the bandwidth, and total treatment effect when radius is of smaller order than the bandwidth. In the more realistic regime where the radius is of similar order as the bandwidth, the RDD estimand is a mixture of the above effects. To recover direct and spillover effects, we propose incorporating estimated spillover terms into the local linear regression -- the local analog of a peer effects regression. We also clarify the settings under which the donut-hole RDD is able to eliminate the effects of spillovers.
"Testing the Fairness-Improvability of Algorithms" (with Annie Liang, Max Tabord-Meehan, and Kyohei Okumura)
Many algorithms have a disparate impact in that their benefits or harms fall disproportionately on certain social groups. Addressing an algorithm's disparate impact can be challenging, however, because it is not always clear whether there exists an alternative more-fair algorithm that does not compromise on other key objectives such as accuracy or profit. Establishing the improvability of algorithms with respect to multiple criteria is of both conceptual and practical interest: in many settings, disparate impact that would otherwise be prohibited under US federal law is permissible if it is necessary to achieve a legitimate business interest. The question is how a policy maker can formally substantiate, or refute, this ``necessity’’ defense. In this paper, we provide an econometric framework for testing the hypothesis that it is possible to improve on the fairness of an algorithm without compromising on other pre-specified objectives. Our proposed test is simple to implement and can incorporate any exogenous constraint on the algorithm space. We establish the large-sample validity and consistency of our test, and demonstrate its use empirically by evaluating a healthcare algorithm originally considered by Obermeyer et al. (2019). In this demonstration, we find strong statistically-significant evidence that it is possible to reduce the algorithm's disparate impact without compromising on the accuracy of its predictions.
"Recovering Network Structure from Aggregated Relational Data using Penalized Regression" (with Hossein Alidaee and Michael P Leung)
Example R and Python code
Social network data can be expensive to collect. Breza et al. (2017) propose aggregated relational data (ARD) as a low-cost substitute that can be used to recover the structure of a latent social network when it is generated by a specific parametric random effects model. Our main observation is that many economic network formation models produce networks that are effectively low-rank. As a consequence, network recovery from ARD is generally possible without parametric assumptions using a nuclear-norm penalized regression. We demonstrate how to implement this method and provide finite-sample bounds on the mean squared error for the resulting estimator for the distribution of network links. Computation takes seconds for samples with hundreds of observations. Easy-to-use code in R and Python can be found here.
"The Local Approach to Causal Inference under Network Interference" (with Max Tabord-Meehan)
Revision requested at Quantitative Economics
We propose a new nonparametric modeling framework for causal inference when outcomes depend on how agents are linked in a social or economic network. Such network interference describes a large literature on treatment spillovers, social interactions, social learning, information diffusion, disease and financial contagion, social capital formation, and more. Our approach works by first characterizing how an agent is linked in the network using the configuration of other agents and connections nearby as measured by path distance. The impact of a policy or treatment assignment is then learned by pooling outcome data across similarly configured agents. We demonstrate the approach by proposing an asymptotically valid test for the hypothesis of policy irrelevance/no treatment effects and bounding the mean-squared error of a k-nearest- neighbor estimator for the average or distributional policy effect/treatment response.
"Identifying Socially Disruptive Policies" (with Yong Cai) [online appendix]
Example R code
Revision requested at The Review of Economic Studies
Social disruption occurs when a policy creates or destroys many network connections between agents. It is a costly side effect of many interventions and so a growing empirical literature recommends measuring and accounting for social disruption when evaluating the welfare impact of a policy. However, there is currently little work characterizing what can actually be learned about social disruption from data in practice. In this paper, we consider the problem of identifying social disruption in a research design that is popular in the literature. We provide two sets of identification results. First, we show that social disruption is not generally point identified, but informative bounds can be constructed using the eigenvalues of the network adjacency matrices observed by the researcher. Second, we show that point identification follows from a theoretically motivated monotonicity condition, and we derive a closed form representation. We apply our methods in two empirical illustrations and find large policy effects that otherwise might be missed by alternatives in the literature.
"Regression Discontinuity Design with Spillovers" (with Yong Cai and Ahnaf Rafi)
Researchers who estimate treatment effects using a regression discontinuity design (RDD) typically assume that there are no spillovers between the treated and control units. This may be unrealistic. We characterize the estimand of RDD in a setting where spillovers occur between units that are close in their values of the running variable. Under the assumption that spillovers are linear-in-means, we show that the estimand depends on the ratio of two terms: (1) the radius over which spillovers occur and (2) the choice of bandwidth used for the local linear regression. Specifically, RDD estimates direct treatment effect when radius is of larger order than the bandwidth, and total treatment effect when radius is of smaller order than the bandwidth. In the more realistic regime where the radius is of similar order as the bandwidth, the RDD estimand is a mixture of the above effects. To recover direct and spillover effects, we propose incorporating estimated spillover terms into the local linear regression -- the local analog of a peer effects regression. We also clarify the settings under which the donut-hole RDD is able to eliminate the effects of spillovers.
"Testing the Fairness-Improvability of Algorithms" (with Annie Liang, Max Tabord-Meehan, and Kyohei Okumura)
Many algorithms have a disparate impact in that their benefits or harms fall disproportionately on certain social groups. Addressing an algorithm's disparate impact can be challenging, however, because it is not always clear whether there exists an alternative more-fair algorithm that does not compromise on other key objectives such as accuracy or profit. Establishing the improvability of algorithms with respect to multiple criteria is of both conceptual and practical interest: in many settings, disparate impact that would otherwise be prohibited under US federal law is permissible if it is necessary to achieve a legitimate business interest. The question is how a policy maker can formally substantiate, or refute, this ``necessity’’ defense. In this paper, we provide an econometric framework for testing the hypothesis that it is possible to improve on the fairness of an algorithm without compromising on other pre-specified objectives. Our proposed test is simple to implement and can incorporate any exogenous constraint on the algorithm space. We establish the large-sample validity and consistency of our test, and demonstrate its use empirically by evaluating a healthcare algorithm originally considered by Obermeyer et al. (2019). In this demonstration, we find strong statistically-significant evidence that it is possible to reduce the algorithm's disparate impact without compromising on the accuracy of its predictions.