Causal Spillover Effects Using Instrumental Variables*

I set up a potential-outcomes framework to analyze spillover effects using instrumental variables. I show that intention-to-treat parameters aggregate a large number of direct and spillover effects for different compliance types, and hence they may not have a clear causal interpretation. I provide three alternative sets of conditions to point identify average direct and spillover effects on specific subpopulations, by restricting either (i) the number of spillover effects, (ii) the degree of noncompliance, or (iii) the degree of heterogeneity in average causal parameters. I propose simple estimators that are consistent and asymptotically normal under mild conditions, and illustrate my results using data from an experiment that analyzes the effect of social interactions in the household on voting behavior.

[1]  Bernard Fortin,et al.  Identification of Peer Effects through Social Networks , 2007, SSRN Electronic Journal.

[2]  Leigh L. Linden,et al.  Improving the Design of Conditional Transfer Programs: Evidence from a Randomized Education Experiment in Colombia † , 2011 .

[3]  M. Blackwell.  Instrumental Variable Methods for Conditional Effects and Causal Interaction in Voter Mobilization Experiments , 2017 .

[4]  Christopher R. Walters,et al.  The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables , 2019, American Economic Review.

[5]  Rocio Titiunik,et al.  Natural Experiments , 2020, Advances in Experimental Political Science.

[6]  Nahomi Ichino,et al.  Deterring or Displacing Electoral Irregularities? Spillover Effects of Observers in a Randomized Field Experiment in Ghana , 2012, The Journal of Politics.

[7]  C. Traxler,et al.  Enforcement Spillovers , 2011, Review of Economics and Statistics.

[8]  Guillaume W. Basse,et al.  A graph‐theoretic approach to randomization tests of causal effects under general interference , 2019, Journal of the Royal Statistical Society: Series B (Statistical Methodology).

[9]  Guillaume W. Basse,et al.  Randomization tests of causal effects under interference , 2019, Biometrika.

[10]  Elie Tamer,et al.  Econometric analysis of models with social interactions , 2020 .

[11]  G. Charness,et al.  Letting Down the Team? Social Effects of Team Incentives , 2012 .

[12]  J. Stock,et al.  Weak Instruments in Instrumental Variables Regression: Theory and Practice , 2019, Annual Review of Economics.

[13]  Alberto Abadie.  Semiparametric instrumental variable estimation of treatment response models , 2003 .

[14]  J. Angrist,et al.  Identification and Estimation of Local Average Treatment Effects , 1994 .

[15]  Bryan S. Graham,et al.  Identifying Social Interactions Through Conditional Variance Restrictions , 2008 .

[16]  Michael E. Sobel,et al.  What Do Randomized Studies of Housing Mobility Demonstrate? , 2006 .

[17]  Dean Eckles,et al.  Estimating peer effects in networks with peer encouragement designs , 2016, Proceedings of the National Academy of Sciences.

[18]  Giacomo De Giorgi,et al.  Identification of Social Interactions through Partially Overlapping Peer Groups , 2010 .

[19]  Betsy Sinclair,et al.  The Social Citizen: Peer Networks and Political Behavior , 2012 .

[20]  J. Heckman,et al.  Unordered Monotonicity , 2017, Econometrica : journal of the Econometric Society.

[21]  J. Aislinn Bohren,et al.  Optimal Design of Experiments in the Presence of Interference , 2017, Review of Economics and Statistics.

[22]  D. Rubin,et al.  Estimating Outcome Distributions for Compliers in Instrumental Variables Models , 1997 .

[23]  R. Moffitt.  Policy Interventions, Low-Level Equilibria, and So-cial Interactions , 1999 .

[24]  Identifying Causal Effects in Experiments with Spillovers and Non-compliance , 2021 .

[25]  G. Imbens,et al.  Peer Encouragement Designs in Causal Inference with Partial Interference and Identification of Local Average Network Effects , 2016, 1609.04464.

[26]  J. Pearl,et al.  Bounds on Treatment Effects from Studies with Imperfect Compliance , 1997 .

[27]  M. Hudgens,et al.  Toward Causal Inference With Interference , 2008, Journal of the American Statistical Association.

[28]  Susan Athey,et al.  The Econometrics of Randomized Experiments , 2016, 1607.00698.

[29]  J. Angrist,et al.  Journal of Economic Perspectives—Volume 15, Number 4—Fall 2001—Pages 69–85 Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments , 2022 .

[30]  P. Rosenbaum.  Interference Between Units in Randomized Experiments , 2007 .

[31]  T. Kitagawa.  A Test for Instrument Validity , 2015 .

[32]  Jason M. Fletcher,et al.  Causal Spousal Health Spillover Effects and Implications for Program Evaluation. , 2017, American economic journal. Economic policy.

[33]  Michael Lawrence Barnett,et al.  Effect of Peer Comparison Letters for High-Volume Primary Care Prescribers of Quetiapine in Older and Disabled Adults: A Randomized Clinical Trial , 2018, JAMA psychiatry.

[34]  Zhichao Jiang,et al.  Causal Inference With Interference and Noncompliance in Two-Stage Randomized Experiments , 2020, Journal of the American Statistical Association.

[35]  Joshua D. Angrist,et al.  Identification of Causal Effects Using Instrumental Variables , 1993 .

[36]  Anna Mikusheva,et al.  Robust Confidence Sets in the Presence of Weak Instruments , 2005 .

[37]  Matias D. Cattaneo,et al.  lpdensity: Local Polynomial Density Estimation and Inference , 2019, J. Stat. Softw..

[38]  Matias D. Cattaneo,et al.  Econometric Methods for Program Evaluation , 2018, Annual Review of Economics.

[39]  E. Duflo,et al.  The Role of Information and Social Interactions in Retirement Plan Decisions: Evidence from a Randomized Experiment , 2002 .

[40]  L. Keele,et al.  An introduction to spillover effects in cluster randomized trials with noncompliance. , 2018, Clinical trials.

[41]  D. Green,et al.  The Effects of Canvassing, Telephone Calls, and Direct Mail on Voter Turnout: A Field Experiment , 2000, American Political Science Review.

[42]  E. D. Rooij,et al.  All in the Family: Partisan Disagreement and Electoral Mobilization in Intimate Networks - A Spillover Experiment , 2017 .

[43]  Gonzalo Vázquez-Baré.  Identification and Estimation of Spillover Effects in Randomized Experiments , 2017, 1711.02745.

[44]  P. John,et al.  How Different Are Telephoning and Canvassing? Results from a ‘Get Out the Vote’ Field Experiment in the British 2005 General Election , 2008, British Journal of Political Science.

[45]  M. Elizabeth Halloran,et al.  Dependent Happenings: a Recent Methodological Review , 2016, Current Epidemiology Reports.

[46]  Joshua D. Angrist,et al.  Mostly Harmless Econometrics: An Empiricist's Companion , 2008 .

[47]  Jean-Marie Dufour,et al.  Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments , 2005 .

[48]  Tyler J VanderWeele,et al.  On causal inference in the presence of interference , 2012, Statistical methods in medical research.

[49]  Esther Duflo,et al.  Do Labor Market Policies Have Displacement Effects? Evidence from a Clustered Randomized Experiment , 2012 .

[50]  J. Angrist,et al.  Identification and Estimation of Local Average Treatment Effects , 1995 .

[51]  Avi Feller,et al.  Analyzing Two-Stage Experiments in the Presence of Interference , 2016, 1608.06805.

[52]  Laurent Davezies,et al.  Identification of Peer Effects Using Group Size Variation , 2006, SSRN Electronic Journal.