Estimating a Continuous Treatment Model with Spillovers: A Control Function Approach

We study a continuous treatment effect model in the presence of treatment spillovers through social networks. We assume that one's outcome is affected not only by his/her own treatment but also by a (weighted) average of his/her neighbors' treatments, both of which are treated as endogenous variables. Using a control function approach with appropriate instrumental variables, we show that the conditional mean potential outcome can be nonparametrically identified. We also consider a more empirically tractable semiparametric model and develop a three-step estimation procedure for this model. As an empirical illustration, we investigate the causal effect of the regional unemployment rate on the crime rate.

[1]  Tadao Hoshino,et al.  Causal Inference with Noncompliance and Unknown Interference , 2021, Journal of the American Statistical Association.

[2]  Wei Biao Wu,et al.  Estimation of nonstationary nonparametric regression model with multiplicative structure , 2021 .

[3]  Federal Reserve Bank of Chicago,et al.  Identifying causal effects in experiments with spillovers and non-compliance , 2020, Journal of Econometrics.

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

[5]  Jane-Ling Wang,et al.  A new approach to varying-coefficient additive models with longitudinal covariates , 2020, Comput. Stat. Data Anal..

[6]  Gonzalo Vázquez-Baré.  Causal Spillover Effects Using Instrumental Variables , 2020, Journal of the American Statistical Association.

[7]  Sukjin Han.  Nonparametric estimation of triangular simultaneous equations models under weak identification , 2020, Quantitative Economics.

[8]  Dean Eckles,et al.  Spillover Effects in Experimental Data , 2020, Advances in Experimental Political Science.

[9]  Yann Bramoullé,et al.  Peer Effects in Networks: A Survey , 2019, Annual Review of Economics.

[10]  Michael P. Leung.  Causal Inference Under Approximate Neighborhood Interference , 2019, SSRN Electronic Journal.

[11]  Laura Forastiere,et al.  Causal Inference on Networks Under Continuous Treatment Interference: An Application to Trade Distortions in Agricultural Markets , 2019, SSRN Electronic Journal.

[12]  Lixia Hu,et al.  Estimation and Identification of a Varying-Coefficient Additive Model for Locally Stationary Processes , 2018, Journal of the American Statistical Association.

[13]  Tadao Hoshino,et al.  Treatment Effect Models with Strategic Interaction in Treatment Decisions , 2018, Journal of Econometrics.

[14]  W. Newey,et al.  Control variables, discrete instruments, and identification of structural functions , 2018, Journal of Econometrics.

[15]  Dena Marie Asta,et al.  The Geometry of Continuous Latent Space Models for Network Data , 2017, Statistical science : a review journal of the Institute of Mathematical Statistics.

[16]  Fredrik Sävje,et al.  AVERAGE TREATMENT EFFECTS IN THE PRESENCE OF UNKNOWN INTERFERENCE. , 2017, Annals of statistics.

[17]  W. Newey,et al.  Semiparametric estimation of structural functions in nonseparable triangular models , 2017, Quantitative Economics.

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

[19]  Takuya Ishihara.  PARTIAL IDENTIFICATION OF NONSEPARABLE MODELS USING BINARY INSTRUMENTS , 2017, Econometric Theory.

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

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

[22]  Xavier D’Haultfœuille,et al.  Identification of Nonseparable Triangular Models With Discrete Instruments , 2015 .

[23]  Alexander Torgovitsky.  Identification of Nonseparable Models Using Instruments With Small Support , 2015 .

[24]  Jane-Ling Wang,et al.  Varying-coefficient additive models for functional data , 2015 .

[25]  Xiaohong Chen,et al.  Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators Under Weak Dependence and Weak Conditions , 2014, 1412.6020.

[26]  Stefan Bauernschuster,et al.  Public Child Care and Mothers' Labor Supply - Evidence from Two Quasi-Experiments , 2013, SSRN Electronic Journal.

[27]  Charles F. Manski,et al.  Identification of Treatment Response with Social Interactions , 2013 .

[28]  Maximilian von Ehrlich,et al.  Generalized Propensity Scores for Multiple Continuous Treatment Variables , 2013, SSRN Electronic Journal.

[29]  Kengo Kato,et al.  Some new asymptotic theory for least squares series: Pointwise and uniform results , 2012, 1212.0442.

[30]  D. Altindag.  Crime and Unemployment: Evidence from Europe , 2012 .

[31]  Runze Li,et al.  NEW EFFICIENT ESTIMATION AND VARIABLE SELECTION METHODS FOR SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS. , 2011, Annals of statistics.

[32]  Maximilian Kasy,et al.  IDENTIFICATION IN TRIANGULAR SYSTEMS USING CONTROL FUNCTIONS , 2010, Econometric Theory.

[33]  Runze Li,et al.  Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression , 2010 .

[34]  I. Prucha,et al.  Central Limit Theorems and Uniform Laws of Large Numbers for Arrays of Random Fields. , 2009, Journal of econometrics.

[35]  H. Zou,et al.  Composite quantile regression and the oracle Model Selection Theory , 2008, 0806.2905.

[36]  Costas Meghir,et al.  Identification of Treatment Effects Using Control Functions in Models with Continuous, Endogenous Treatment and Heterogeneous Effects , 2008 .

[37]  Ming-Jen Lin,et al.  Does Unemployment Increase Crime?: Evidence from U.S. Data 1974-2000 , 2008 .

[38]  Lijian Yang,et al.  Spline-backfitted kernel smoothing of nonlinear additive autoregression model , 2006, math/0612677.

[39]  Andrew Gelman,et al.  Applied Bayesian Modeling And Causal Inference From Incomplete-Data Perspectives , 2005 .

[40]  Kosuke Imai,et al.  Causal Inference With General Treatment Regimes , 2004 .

[41]  Joel L. Horowitz,et al.  Nonparametric Estimation of an Additive Quantile Regression Model , 2004 .

[42]  Jianhua Z. Huang.  Local asymptotics for polynomial spline regression , 2003 .

[43]  G. Imbens,et al.  Identification and Estimation of Triangular Simultaneous Equations Models without Additivity , 2002 .

[44]  Joel L. Horowitz,et al.  Nonparametric estimation of an additive model with a link function , 2002, math/0508595.

[45]  Steven D. Levitt,et al.  Alternative Strategies for Identifying the Link Between Unemployment and Crime , 2001 .

[46]  Preliminary version prepared for the Econometric Society World Meetings , 2000 .

[47]  Steven Raphael,et al.  Identifying the Effect of Unemployment on Crime* , 2001, The Journal of Law and Economics.

[48]  O. Linton,et al.  A kernel method of estimating structured nonparametric regression based on marginal integration , 1995 .

[49]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[50]  Noel A. C. Cressie,et al.  Statistics for Spatial Data: Cressie/Statistics , 1993 .

[51]  C. Manski.  Identification of Endogenous Social Effects: The Reflection Problem , 1993 .

[52]  C. J. Stone,et al.  Optimal Global Rates of Convergence for Nonparametric Regression , 1982 .

[53]  Spillover Effects , 2021, Encyclopedia of Evolutionary Psychological Science.

[54]  Xiaohong Chen.  Chapter 76 Large Sample Sieve Estimation of Semi-Nonparametric Models , 2007 .