The identification region of the potential outcome distributions under instrument independence

This paper examines identification power of the instrument exogeneity assumption in the treatment effect model. We derive the identification region: The set of potential outcome distributions that are compatible with data and the model restriction. The model restrictions whose identifying power is investigated are (i)instrument independence of each of the potential outcome (marginal independence), (ii) instrument joint independence of the potential outcomes and the selection heterogeneity, and (iii) instrument monotonicity in addition to (ii) (the LATE restriction of Imbens and Angrist (1994)), where these restrictions become stronger in the order of listing. By comparing the size of the identification region under each restriction, we show that the joint independence restriction can provide further identifying information for the potential outcome distributions than marginal independence, but the LATE restriction never does since it solely constrains the distribution of data. We also derive the tightest possible bounds for the average treatment effects under each restriction. Our analysis covers both the discrete and continuous outcome case, and extends the treatment effect bounds of Balke and Pearl(1997) that are available only for the binary outcome case to a wider range of settings including the continuous outcome case.

[1]  Charles F. Manski,et al.  Identification for Prediction and Decision , 2008 .

[2]  Judea Pearl,et al.  From Bayesian networks to causal networks , 1995 .

[3]  Charles F. Manski,et al.  The Selection Problem , 1990 .

[4]  Yanqin Fan.  Sharp Bounds on the Distribution of the Treatment E ¤ ects and Their Statistical Inference , 2006 .

[5]  Jinyong Hahn,et al.  Bounds on ATE with discrete outcomes , 2010 .

[6]  Toru Kitagawa,et al.  Testing for Instrument Independence in the Selection Model , 2009 .

[7]  Andrew Chesher,et al.  Nonparametric Identification under Discrete Variation , 2003 .

[8]  Edward Vytlacil,et al.  Local Instrumental Variables , 2000 .

[9]  Judea Pearl,et al.  On the Testability of Causal Models With Latent and Instrumental Variables , 1995, UAI.

[10]  Ilya Molchanov,et al.  Partial identification using random set theory , 2010, Journal of Econometrics.

[11]  G. Imbens,et al.  Identi cation and Inference in Nonlinear Di ¤ erence-InDi ¤ erences Models , 2006 .

[12]  James J. Heckman,et al.  Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Econometric Estimators to Evaluate Social Programs, and to Forecast their Effects in New Environments , 2007 .

[13]  C. Manski.  Partial Identification of Probability Distributions , 2003 .

[14]  J. Angrist,et al.  Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings , 1999 .

[15]  J. Heckman,et al.  Instrumental Variables, Selection Models, and Tight Bounds on the Average Treatment Effect , 2000 .

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

[17]  Geert Ridder,et al.  Bounds on Functionals of the Distribution of Treatment Effects , 2008 .

[18]  Yanqin Fan,et al.  SHARP BOUNDS ON THE DISTRIBUTION OF TREATMENT EFFECTS AND THEIR STATISTICAL INFERENCE , 2009, Econometric Theory.

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

[20]  J. Heckman,et al.  Making the Most out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts , 1997 .

[21]  D. Rubin,et al.  Identification of Causal Effects Using Instrumental Variables: Rejoinder , 1996 .

[22]  E. Vytlacil.  Independence, Monotonicity, and Latent Index Models: An Equivalence Result , 2002 .

[23]  C. Manski.  Nonparametric Bounds on Treatment Effects , 1989 .

[24]  E. Vytlacil,et al.  Treatment Effect Bounds under Monotonicity Assumptions: An Application to Swan-Ganz Catheterization , 2008 .

[25]  Charles F. Manski,et al.  Social Choice with Partial Knowledge of Treatment Response , 2020 .

[26]  Andrew Chesher,et al.  Instrumental Variable Models for Discrete Outcomes , 2008 .