Local Average and Quantile Treatment Effects Under Endogeneity: A Review

References

Abadie, A. 2002. “Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models.” Journal of the American Statistical Association 97: 284–292.10.1198/016214502753479419Search in Google Scholar

Abadie, A. 2003. “Semiparametric Instrumental Variable Estimation of Treatment Response Models.” Journal of Econometrics 113: 231–263.10.1016/S0304-4076(02)00201-4Search in Google Scholar

Abadie, A., J. Angrist, and G. W. Imbens. 2002. “Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings.” Econometrica 70: 91–117.10.1111/1468-0262.00270Search in Google Scholar

Aizer, A., and J. J. Doyle. 2013. “Juvenile Incarceration, Human Capital and Future Crime: Evidence from Randomly-Assigned Judges.” Technical report, NBER.10.3386/w19102Search in Google Scholar

Aliprantis, D. 2012. “Redshirting, Compulsory Schooling Laws, and Educational Attainment.” Journal of Educational and Behavioral Statistics 37: 316–338.10.26509/frbc-wp-201012Search in Google Scholar

Andresen, M. E., and M. Huber. 2018. “Instrument-based Estimation with Binarized Treatments: Issues and Tests for the Exclusion Restriction.” SES Working Paper 492, University of Fribourg.Search in Google Scholar

Angrist, J. 1990. “Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records.” American Economic Review 80: 313–336.Search in Google Scholar

Angrist, J., and W. Evans. 1998. “Children and their Parents Labor Supply: Evidence from Exogeneous Variation in Family Size.” American Economic Review 88: 450–477.10.3386/w5778Search in Google Scholar

Angrist, J., and I. Fernández-Val. 2010. “Extrapolate-ing: External Validity and Overidentification in the Late Framework.” NBER working paper 16566.10.3386/w16566Search in Google Scholar

Angrist, J., and G. W. Imbens. 1995. “Two-Stage Least Squares Estimation of Average Causal Effects in Models with Variable Treatment Intensity.” Journal of American Statistical Association 90: 431–442.10.1080/01621459.1995.10476535Search in Google Scholar

Angrist, J., G. W. Imbens, and D. Rubin. 1996. “Identification of Causal Effects Using Instrumental Variables.” Journal of American Statistical Association 91: 444–472 (with discussion).10.3386/t0136Search in Google Scholar

Angrist, J., and A. Krueger. 1991. “Does Compulsory School Attendance Affect Schooling and Earnings?” Quarterly Journal of Economics 106: 979–1014.10.3386/w3572Search in Google Scholar

Angrist, J. D. 2004. “Treatment Effect Heterogeneity in Theory and Practice.” The Economic Journal 114: C52–C83.10.3386/w9708Search in Google Scholar

Angrist, J. D., and J.-S. Pischke. 2009. Mostly Harmless Econometrics: An Epiricist’s Companion. Princeton University Press.10.1515/9781400829828Search in Google Scholar

Angrist, J. D., and J.-S. Pischke. 2015. Mastering ’Metrics: The Path from Cause to Effect, Princeton: Princeton University Press.Search in Google Scholar

Aronow, P. M., and A. Carnegie. 2013. “Beyond Late: Estimation of the Average Treatment Effect with an Instrumental Variable.” Political Analysis 21: 492–506.10.1093/pan/mpt013Search in Google Scholar

Balke, A., and J. Pearl. 1997. “Bounds on Treatment Effects from Studies with Imperfect Compliance.” Journal of the American Statistical Association 92: 1171–1176.10.1080/01621459.1997.10474074Search in Google Scholar

Barua, R., and K. Lang. 2009. “School Entry, Educational Attainment, and Quarter of Birth: A Cautionary Tale of Late.” NBER Working Paper 15236.10.3386/w15236Search in Google Scholar

Battistin, E., M. De Nadai, and B. Sianesi. 2014. “Misreported Schooling, Multiple Measures and Returns to Educational Qualifications.” Journal of Econometrics 181: 136–150.10.1016/j.jeconom.2014.03.002Search in Google Scholar

Bedard, K., and E. Dhuey. 2006. “The Persistence of Early Childhood Maturity: International Evidence of Long-Run Age Effects.” The Quarterly Journal of Economics 121: 1437–1472.10.1093/qje/121.4.1437Search in Google Scholar

Behaghel, L., B. Crépon, and M. Gurgand. 2013. “Robustness of the Encouragement Design in a Two-Treatment Randomized Control Trial.” IZA Discussion Paper No 7447.10.2139/ssrn.2283562Search in Google Scholar

Belloni, A., V. Chernozhukov, I. Fernández-Val, and C. Hansen. 2017. “Program Evaluation and Causal Inference with High-Dimensional Data.” Econometrica 85: 233–298.10.1920/wp.cem.2016.1316Search in Google Scholar

Bertanha, M., and G. Imbens. 2015. “External Validity in Fuzzy Regression Discontinuity Designs.” NBER working paper 20773.10.3386/w20773Search in Google Scholar

Black, D. A., J. Joo, R. J. LaLonde, J. A. Smith, and E. J. Taylor. 2015. “Simple Tests for Selection Bias: Learning More from Instrumental Variables.” IZA Discussion Paper No 9346.10.2139/ssrn.2663776Search in Google Scholar

Blackwell, M. 2015. “Identification and Estimation of Joint Treatment Effects with Instrumental Variables.” working paper, Department of Government, Harvard University.Search in Google Scholar

Bloom, H. S. 1984. “Accounting for No-Shows in Experimental Evaluation Designs.” Evaluation Review 8: 225–246.10.1177/0193841X8400800205Search in Google Scholar

Bound, J., D. A. Jaeger, and R. M. Baker. 1995. “Problems with Instrumental Variables Estimation When the Correlation Between the Instruments and the Endogeneous Explanatory Variable is Weak.” Journal of the American Statistical Association 90: 443–450.10.2307/2291055Search in Google Scholar

Brinch, C. N., M. Mogstad, and M. Wiswall. 2017. “Beyond Late with a Discrete Instrument.” Journal of Political Economy 125: 985–1039.10.1086/692712Search in Google Scholar

Buckles, K. S., and D. M. Hungerman. 2013. “Season of Birth and Later Outcomes: Old Questions, New Answers.” Review of Economics and Statistics 95: 711–724.10.3386/w14573Search in Google Scholar

Card, D. 1995. “Using Geographic Variation in College Proximity to Estimate the Return to Schooling.” In Aspects of Labor Market Behaviour: Essays in Honour of John Vanderkamp, edited by L. Christofides, E. Grant, and R. Swidinsky, 201–222. Toronto: University of Toronto Press.Search in Google Scholar

Card, D., and T. Lemieux. 2001. “Going to College to Avoid the Draft: The Unintended Legacy of the Vietnam War.” The American Economic Review 91: 97–102.10.1257/aer.91.2.97Search in Google Scholar

Carneiro, P., J. J. Heckman, and E. J. Vytlacil. 2011. “Estimating Marginal Returns to Education.” American Economic Review 101: 2754–2781.10.1257/aer.101.6.2754Search in Google Scholar PubMed PubMed Central

Carneiro, P., and S. Lee. 2009. “Estimating Distributions of Potential Outcomes Using Local Instrumental Variables With an Application to Changes in College Enrollment and Wage Inequality.” Journal of Econometrics 149 (2): 191–208.10.1016/j.jeconom.2009.01.011Search in Google Scholar

Chalak, K. 2016 . “Instrumental Variables Methods with Heterogeneity and Mismeasured Instruments.” Econometric Theory 33: 1– 36.10.1017/S0266466615000390Search in Google Scholar

Chalak, K., and H. White. 2011. “An Extended Class of Instrumental Variables for the Estimation of Causal Effects.” Canadian Journal of Economics 44: 1–51.10.1111/j.1540-5982.2010.01622.xSearch in Google Scholar

Chen, X., and C. A. Flores. 2015. “Bounds on Treatment Effects in the Presence of Sample Selection and Noncompliance: The Wage Effects of Job Corps.” Journal of Business & Economic Statistics 33: 523–540.10.1080/07350015.2014.975229Search in Google Scholar

Chen, X., C. A. Flores, and A. Flores-Lagunes. 2017. “Going Beyond Late: Bounding Average Treatment Effects of Job Corps Training.” Journal of Human Resources. DOI: 10.3368/jhr.53.4.1015.7483R1.Search in Google Scholar

Cheng, J., and D. S. Small. 2006. “Bounds on Causal Effects in Three-Arm Trials with Non-compliance.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68: 815–836.10.1111/j.1467-9868.2006.00568.xSearch in Google Scholar

Chernozhukov, V., D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W. Newey, and J. Robins. 2017. “Double/Debiased Machine Learning for Treatment and Structural Parameters.” Econometrics Journal 21: C1–C68.10.3386/w23564Search in Google Scholar

Chernozhukov, V., and C. Hansen. 2005. “An IV Model of Quantile Treatment Effects.” Econometrica 73: 245–261.10.1111/j.1468-0262.2005.00570.xSearch in Google Scholar

Chernozhukov, V., S. Lee, and A. Rosen. 2013. “Intersection Bounds: Estimation and Inference.” Econometrica 81: 667–737.10.1920/wp.cem.2012.3312Search in Google Scholar

Chiburis, R. C. 2010. “Semiparametric Bounds on Treatment Effects.” Journal of Econometrics 159: 267–275.10.1016/j.jeconom.2010.07.006Search in Google Scholar

Conley, T. G., C. B. Hansen, and P. E. Rossi. 2012. “Plausibly Exogenous.” Review of Economics and Statistics 94: 260–272.10.1162/REST_a_00139Search in Google Scholar

Cornelissen, T., C. Dustmann, A. Raute, and S. Uta. 2016. “From Late to MTE: Alternative Methods for the Evaluation of Policy Interventions.” IZA DP No. 10056.10.2139/ssrn.2818310Search in Google Scholar

Dahl, C. M., M. Huber, and G. Mellace. 2016. “It’s Never Too Late. A New Look at the Identification of Local Average Treatment Effects with or Without Defiers.” working paper, University of Southern Denmark, Dept. of Economics.10.2139/ssrn.2916599Search in Google Scholar

de Chaisemartin, C. 2016. “Tolerating Defiance? Identification of Treatment Effects Without Monotonicity.” working paper, University of Warwick.10.3982/QE601Search in Google Scholar

de Luna, X., and P. Johansson. 2014. “Testing for the Unconfoundedness Assumption Using an Instrumental Assumption.” Journal of Causal Inference 2: 187–199.10.1515/jci-2013-0011Search in Google Scholar

Deaton, A. S. 2010. “Instruments, Randomization, and Learning about Development.” Journal of Economic Literature 48: 424–455.10.12987/9780300199307-008Search in Google Scholar

DiNardo, J., and D. S. Lee. 2011. “Program Evaluation and Research Designs,” In Handbook of Labor Economics, edited by Orley Ashenfelter, and David Card, Vol. 4, 463–536. New York: Elsevier.10.1016/S0169-7218(11)00411-4Search in Google Scholar

DiTraglia, F., and C. Garcia-Jimeno. 2016. “On Mis-Measured Binary Regressors: New Results and Some Comments on the Literature.” working paper, University of Pennsylvania.10.2139/ssrn.2684610Search in Google Scholar

Donald, S. G., Y.-C. Hsu, and R. P. Lieli. 2014a. “Inverse Probability Weighted Estimation of Local Average Treatment Effects: A Higher Order MSE Expansion.” Statistics and Probability Letters 95: 132–138.10.1016/j.spl.2014.08.015Search in Google Scholar

Donald, S. G., Y.-C. Hsu, and R. P. Lieli. 2014b. “Testing the Unconfoundedness Assumption via Inverse Probability Weighted Estimators of (L)ATT.” Journal of Business & Economic Statistics 32 (3): 395–415.10.1080/07350015.2014.888290Search in Google Scholar

Dzemski, A., and F. Sarnetzki. 2014. “Overidentification Test in a Nonparametric Treatment Model with Unobserved Heterogeneity.” mimeo, University of Mannheim.Search in Google Scholar

Fiorini, M., and K. Stevens. 2014. “Monotonicity in IV and fuzzy RD designs - A Guide to Practice.” mimeo, University of Sydney.Search in Google Scholar

Flores, C. A., and A. Flores-Lagunes. 2013. “Partial Identification of Local Average Treatment Effects With an Invalid Instrument.” Journal of Business & Economic Statistics 31: 534–545.10.1080/07350015.2013.822760Search in Google Scholar

Frangakis, C., and D. Rubin. 1999. “Addressing Complications of Intention-to-Treat Analysis in the Combined Presence of All-or-None Treatment-Noncompliance and Subsequent Missing Outcomes.” Biometrika 86: 365–379.10.1093/biomet/86.2.365Search in Google Scholar

Fricke, H., M. Frölich, M. Huber, and M. Lechner. 2015. “Endogeneity and Non-Response Bias in Treatment Evaluation: Nonparametric Identification of Causal Effects by Instruments.” IZA Discussion Paper No 9428.10.2139/ssrn.2675485Search in Google Scholar

Frölich, M. 2007. “Nonparametric IV Estimation of Local Average Treatment Effects with Covariates.” Journal of Econometrics 139: 35–75.10.1016/j.jeconom.2006.06.004Search in Google Scholar

Frölich, M., and M. Huber. 2014. “Treatment Evaluation with Multiple Outcome Periods Under Endogeneity and Attrition.” Journal of the American Statistical Association 109: 1697–1711.10.1080/01621459.2014.896804Search in Google Scholar

Frölich, M., and M. Huber. 2017. “Direct and Indirect Treatment Effects - Causal Chains and Mediation Analysis with Instrumental Variables.” Journal of the Royal Statistical Society Series B 79: 1645–1666.10.1111/rssb.12232Search in Google Scholar

Frölich, M., and M. Lechner. 2015. “Combining Matching and Nonparametric Instrumental Variable Estimation: Theory and an Application to the Evaluation of Active Labour Market Policies.” Journal of Applied Econometrics 30: 718–738.10.1002/jae.2417Search in Google Scholar

Frölich, M., and B. Melly. 2013a. “Identification of Treatment Effects on the Treated with One-Sided Non-Compliance.” Econometric Reviews 32: 384–414.10.1080/07474938.2012.718684Search in Google Scholar

Frölich, M., and B. Melly. 2013b. “Unconditional Quantile Treatment Effects Under Endogeneity.” Journal of Business & Economic Statistics 31: 346–357.10.1080/07350015.2013.803869Search in Google Scholar

Frumento, P., F. Mealli, B. Pacini, and D. B. Rubin. 2012. “Evaluating the Effect of Training on Wages in the Presence of Noncompliance, Nonemployment, and Missing Outcome Data.” Journal of the American Statistical Association 107: 450–466.10.1080/01621459.2011.643719Search in Google Scholar

Hausman, J. A. 1978. “Specification Tests in Econometrics.” Econometrica 46: 1251–1271.10.2307/1913827Search in Google Scholar

Heckman, J. J. 1997. “Instrumental Variables: A Study of Implicit Behavioral Assumptions Used in Making Program Evaluations.” The Journal of Human Resources 32: 441–462.10.2307/146178Search in Google Scholar

Heckman, J. J., and R. Pinto. 2018. “Unordered Monotonicity.” Econometrica 86: 1–35.10.3386/w23497Search in Google Scholar

Heckman, J. J., D. Schmierer, and S. Urzua. 2010. “Testing the Correlated Random Coefficient Model.” Journal of Econometrics 158: 177–203.10.3386/w15463Search in Google Scholar

Heckman, J. J., and S. Urzúa. 2010. “Comparing IV with Structural Models: What Simple IV Can and Cannot Identify.” Journal of Econometrics 156: 27–37.10.3386/w14706Search in Google Scholar

Heckman, J. J., and E. Vytlacil. 1999. “Local Instrumental Variables and Latent Variable Models for Identifying and Bounding Treatment Effects.” Proceedings National Academic Sciences USA, Economic Sciences 96, 4730–4734.10.1073/pnas.96.8.4730Search in Google Scholar

Heckman, J. J., and E. Vytlacil. 2001a. “Instrumental Variables, Selection Models, and Tight Bounds on the Average Treatment Effects.” In Econometric Evaluation of Labour Market Policies, edited by M. Lechner, M. Pfeiffer, 1–15. New York: Center for European Economic Research.10.1007/978-3-642-57615-7_1Search in Google Scholar

Heckman, J. J., and E. Vytlacil. 2001b. “Local Instrumental Variables.” In Nonlinear Statistical Inference: Essays in Honor of Takeshi Amemiya, edited by C. Hsiao, K. Morimune, J. Powell. Cambridge: Cambridge University Press.10.1017/CBO9781139175203.003Search in Google Scholar

Heckman, J. J., and E. Vytlacil. 2005. “Structural Equations, Treatment Effects, and Econometric Policy Evaluation 1.” Econometrica 73: 669–738.10.1111/j.1468-0262.2005.00594.xSearch in Google Scholar

Heckman, J. J., and E. J. Vytlacil. 2007. “Chapter 71 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.” In Part B of Handbook of Econometrics, edited by James J. Heckman, Edward E. Leamer, Vol. 6, 4875–5143. North-Holland: Elsevier.10.1016/S1573-4412(07)06071-0Search in Google Scholar

Hernan, M. A., and J. M. Robins. 2006. “Instruments for Causal Inference. An Epidemiologist’s Dream?” Epidemiology 17: 360–372.10.1097/01.ede.0000222409.00878.37Search in Google Scholar PubMed

Hirano, K., G. W. Imbens, and G. Ridder. 2003. “Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score.” Econometrica 71: 1161–1189.10.3386/t0251Search in Google Scholar

Hong, H., and D. Nekipelov. 2010. “Semiparametric Efficiency in Nonlinear Late Models.” Quantitative Economics 1: 279–304.10.3982/QE43Search in Google Scholar

Hsu, Y.-C., T.-C. Lai, and R. P. Lieli. Estimation and Inference for Distribution Functions and Quantile Functions in Endogenous Treatment Effect Models 2015 Working Paper, Central European University.Search in Google Scholar

Huber, M. 2013. “A Simple Test for the Ignorability of Non-Compliance in Experiments.” Economics Letters 120: 389–391.10.1016/j.econlet.2013.05.018Search in Google Scholar

Huber, M. 2014. Sensitivity Checks for the Local Average Treatment Effect.” Economics Letters 123: 220–223.10.1016/j.econlet.2014.02.018Search in Google Scholar

Huber, M., L. Laffers, and G. Mellace. 2017. “Sharp IV Bounds on Average Treatment Effects on the Treated and Other Populations Under Endogeneity and Noncompliance.” Journal of Applied Econometrics 32: 56–79.10.1002/jae.2473Search in Google Scholar

Huber, M., and G. Mellace. 2015. “Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints.” Review of Economics and Statistics 97: 398–411.10.1162/REST_a_00450Search in Google Scholar

Hull, P. 2015. “Isolateing: Identifying Counterfactual-Specific Treatment Effects with Cross-Stratum Comparisons.” working paper, MIT Department of Economics.10.2139/ssrn.2705108Search in Google Scholar

Imbens, G. W. 2004. “Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review.” The Review of Economics and Statistics 86: 4–29.10.3386/t0294Search in Google Scholar

Imbens, G. W. 2010. “Better LATE Than Nothing: Some Comments on Deaton (2009) and Heckman and Urzua (2009).” Journal of Economic Literature 48 (2): 399–423.10.3386/w14896Search in Google Scholar

Imbens, G. W. 2014. “Instrumental Variables: An Econometrician’s Perspective.” IZA Discussion Paper No. 8048.10.3386/w19983Search in Google Scholar

Imbens, G. W., and J. Angrist. 1994. “Identification and Estimation of Local Average Treatment Effects.” Econometrica 62: 467–475.10.2307/2951620Search in Google Scholar

Imbens, G. W., and D. Rubin. 1997. “Estimating Outcome Distributions for Compliers in Instrumental Variables Models.” Review of Economic Studies 64: 555–574.10.2307/2971731Search in Google Scholar

Imbens, G. W., and J. M. Wooldridge. 2009. “Recent Developments in the Econometrics of Program Evaluation.” Journal of Economic Literature 47: 5–86.10.3386/w14251Search in Google Scholar

Jones, D. 2015. “The Economics of Exclusion Restrictions in IV Models.” NBER working paper 21391, Cambridge, MA.10.3386/w21391Search in Google Scholar

Kédagni, D., and I. Mourifié. 2016. “Empirical Content of the IV Zero-Covariance Assumption: Testability, Partial Identification.” working paper, University of Toronto.Search in Google Scholar

Kirkeboen, L., E. Leuven, and M. Mogstad. 2016. “Fields of Study, Earnings, and Self-Selection.” Quarterly Journal of Economics 131: 1057–1111.10.3386/w20816Search in Google Scholar

Kitagawa, T. 2009. “Identification Region of the Potential Outcome Distribution Under Instrument Independence.” CeMMAP working paper 30/09.10.1920/wp.cem.2009.3009Search in Google Scholar

Kitagawa, T. 2015. “A Test for Instrument Validity.” Econometrica 83: 2043–2063.10.1920/wp.cem.2014.3414Search in Google Scholar

Klein, T. J. 2010. “Heterogeneous Treatment Effects: Instrumental Variables Without Monotonicity?” Journal of Econometrics 155: 99–116.10.1016/j.jeconom.2009.08.006Search in Google Scholar

Kolesar, M. 2013. Estimation in an Instrumental Variable Model with Treatment Effect Heterogeneity, Working Paper, Princeton University.Search in Google Scholar

Kowalski, A. E. 2016. “Doing More When You’re Running Late: Applying Marginal Treatment Effect Methods to Examine Treatment Effect Heterogeneity in Experiments.” working paper, Yale University.10.3386/w22363Search in Google Scholar

Lee, J. 2008. “Sibling Size and Investment in Children’s Education: An Asian Instrument.” Journal of Population Economics 21: 855–875.10.1007/s00148-006-0124-5Search in Google Scholar

Lee, S., and B. Salanie. 2015. “Identifying Effects of Multivalued Treatments.” cemmap working paper CWP72/15.10.1920/wp.cem.2015.7215Search in Google Scholar

Little, R., and D. Rubin. 1987. Statistical Analysis with Missing Data. New York: Wiley.Search in Google Scholar

Machado, C., A. Shaikh, and E. Vytlacil. 2018. Instrumental Variables, and the Sign of the Average Treatment Effect, Working Paper, University of Chicago.10.2139/ssrn.3334009Search in Google Scholar

Maestas, N., K. J. Mullen, and A. Strand. 2013. “Does Disability Insurance Receipt Discourage Work? Using Examiner Assignment to Estimate Causal Effects of SSDI Receipt.” The American Economic Review 103: 1797–1829.10.1257/aer.103.5.1797Search in Google Scholar

Manski, C. F. 1990. “Nonparametric Bounds on Treatment Effects.” American Economic Review, 319–323. Papers and Proceedings 80.Search in Google Scholar

Marshall, J. 2016. “Coarsening Bias: How Coarse Treatment Measurement Upwardly Biases Instrumental Variable Estimates.” Political Analysis 24: 157–171.10.1093/pan/mpw007Search in Google Scholar

Mealli, F., G. Imbens, S. Ferro, and A. Biggeri. 2004. “Analyzing a Randomized Trial on Breast Self-examination with Noncompliance and Missing Outcomes.” Biostatistics 5: 207–222.10.1093/biostatistics/5.2.207Search in Google Scholar PubMed

Mealli, F., and B. Pacini. 2013. “Using Secondary Outcomes and Covariates to Sharpen Inference in Instrumental Variable Settings.” Journal of the American Statistical Association 108: 1120–1131.10.1080/01621459.2013.802238Search in Google Scholar

Melly, Blaise, and Kaspar Wüthrich. 2018. “Local Quantile Treatment Effects,” In Handbook of Quantile Regression, edited by Roger Koenker, Victor Chernozhukov, Xiuming He, and Limin Peng, 145–164. Chapman and Hall/CRC.10.1201/9781315120256-10Search in Google Scholar

Miquel, R. 2002. “Identification of Dynamic Treatment Effects by Instrumental Variables.” University of St. Gallen Economics Discussion Paper Series 2002–2011.Search in Google Scholar

Mogstad, M., A. Santos, and A. Torgovitsky. 2017. Using Instrumental Variables for Inference about Policy Relevant Treatment Effects, NBER Working Paper No. 23568.10.3386/w23568Search in Google Scholar

Mourifié, I., and Y. Wan. 2017. “Testing Late Assumptions.” The Review of Economics and Statistics 99: 305–313.10.2139/ssrn.2429664Search in Google Scholar

Richardson, T. S., and J. M. Robins. 2010. “Analysis of the Binary Instrumental Variable Model.” In Heuristics, Probability and Causality: A Tribute to Judea Pearl, edited by R. Dechter, H. Geffner, and J. Y. Halpern, 415–440. London, UK: College Publications.Search in Google Scholar

Rosenbaum, P., and D. Rubin. 1983. “The Central Role of the Propensity Score in Observational Studies for Causal Effects.” Biometrika 70: 41–55.10.21236/ADA114514Search in Google Scholar

Roy, A. 1951. “Some Thoughts on the Distribution of Earnings.” Oxford Economic Papers 3: 135–146.10.1093/oxfordjournals.oep.a041827Search in Google Scholar

Rubin, D. B. 1974. “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies.” Journal of Educational Psychology 66: 688–701.10.1037/h0037350Search in Google Scholar

Rubin, D. B. 1976. “Inference and Missing Data.” Biometrika 63: 581–592.10.1093/biomet/63.3.581Search in Google Scholar

Shaikh, A., and E. Vytlacil. 2011. “Partial Identification in Triangular Systems of Equations with Binary Dependent Variables.” Econometrica 79: 949–955.10.3982/ECTA9082Search in Google Scholar

Sharma, A. 2016. “Necessary and Probably Sufficient Test for Finding Valid Instrumental Variables.” working paper, Microsoft Research, New York.Search in Google Scholar

Slichter, D. 2014. Testing Instrument Validity and Identification with Invalid Instruments. Mimeo: University of Rochester.Search in Google Scholar

Small, D. S., and Z. Tan. 2007. “A Stochastic Monotonicity Assumption for the Instrumental Variables Method.” Technical report, Department of Statistics, Wharton School, University of Pennsylvania.Search in Google Scholar

Small, D. S., Z. Tan, R. R. R. S. A. Lorch, and M. A. Brookhart. 2017. “Instrumental Variable Estimation with a Stochastic Monotonicity Assumption.” Statistical Science 32: 561–579.10.1214/17-STS623Search in Google Scholar

Tan, Z. 2006. “Regression and Weighting Methods for Causal Inference Using Instrumental Variables.” Journal of the American Statistical Association 101: 1607–1618.10.1198/016214505000001366Search in Google Scholar

Ura, T. 2016. “Heterogeneous Treatment Effects with Mismeasured Endogenous Treatment.” working paper, Duke University.Search in Google Scholar

Uysal, S. D. 2011. Doubly Robust IV Estimation of the Local Average Treatment Effects. Mimeo: University of Konstanz.Search in Google Scholar

Vuong, Q., and H. Xu. 2017. “Counterfactual Mapping and Individual Treatment Effects in Nonseparable Models with Binary Endogeneity.” Quantitative Economics 8 (2): 589–610.10.3982/QE579Search in Google Scholar

Vytlacil, E. 2002. “Independence, Monotonicity, and Latent Index Models: An Equivalence Result.” Econometrica 70: 331–341.10.1111/1468-0262.00277Search in Google Scholar

Wüthrich, Kaspar 2018. “A Comparison of Two Quantile Models with Endogeneity.” Journal of Business and Economic Statistics, Accepted for publication.10.1080/07350015.2018.1514307Search in Google Scholar

Yamamoto, T. 2013. “Identification and Estimation of Causal Mediation Effects with Treatment Noncompliance.” unpublished manuscript, MIT Department of Political Science.Search in Google Scholar

Yanagi, T. 2017. “Inference on Local Average Treatment Effects for Misclassified Treatment.” working paper, Hitotsubashi University, Tokyo.10.2139/ssrn.3065923Search in Google Scholar

Yu, P. 2014. Marginal Quantile Treatment Effect and Counterfactual Analysis, Working Paper, The University of Hong Kong.Search in Google Scholar

Zhang, J., D. Rubin, and F. Mealli. 2009. “Likelihood-Based Analysis of Causal Effects of Job-Training Programs Using Principal Stratification.” Journal of the American Statistical Association 104: 166–176.10.1198/jasa.2009.0012Search in Google Scholar