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Testing Instrument Validity with Covariates

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  • Thomas Carr
  • Toru Kitagawa

Abstract

We develop a novel test of the instrumental variable identifying assumptions for heterogeneous treatment effect models with conditioning covariates. We assume semiparametric dependence between potential outcomes and conditioning covariates. This allows us to obtain testable equality and inequality restrictions among the subdensities of estimable partial residuals. We propose jointly testing these restrictions. To improve power, we introduce distillation, where a trimmed sample is used to test the inequality restrictions. In Monte Carlo exercises we find gains in finite sample power from testing restrictions jointly and distillation. We apply our test procedure to three instruments and reject the null for one.

Suggested Citation

  • Thomas Carr & Toru Kitagawa, 2021. "Testing Instrument Validity with Covariates," Papers 2112.08092, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2112.08092
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    References listed on IDEAS

    as
    1. Damon Clark & Heather Royer, 2013. "The Effect of Education on Adult Mortality and Health: Evidence from Britain," American Economic Review, American Economic Association, vol. 103(6), pages 2087-2120, October.
    2. Martin Huber, 2015. "Testing the Validity of the Sibling Sex Ratio Instrument," LABOUR, CEIS, vol. 29(1), pages 1-14, March.
    3. Cruces, Guillermo & Galiani, Sebastian, 2007. "Fertility and female labor supply in Latin America: New causal evidence," Labour Economics, Elsevier, vol. 14(3), pages 565-573, June.
    4. Thomas Cornelissen & Christian Dustmann & Anna Raute & Uta Schönberg, 2018. "Who Benefits from Universal Child Care? Estimating Marginal Returns to Early Child Care Attendance," Journal of Political Economy, University of Chicago Press, vol. 126(6), pages 2356-2409.
    5. Banerjee, Abhijit & Duflo, Esther & Qian, Nancy, 2020. "On the road: Access to transportation infrastructure and economic growth in China," Journal of Development Economics, Elsevier, vol. 145(C).
    6. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2018. "Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters," Econometrica, Econometric Society, vol. 86(5), pages 1589-1619, September.
    7. Stephen V. Cameron & Christopher Taber, 2004. "Estimation of Educational Borrowing Constraints Using Returns to Schooling," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 132-182, February.
    8. Gordon B. Dahl & Enrico Moretti, 2008. "The Demand for Sons," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(4), pages 1085-1120.
    9. Zhenting Sun, 2020. "Instrument Validity for Heterogeneous Causal Effects," Papers 2009.01995, arXiv.org, revised Oct 2023.
    10. Philip Oreopoulos, 2006. "Estimating Average and Local Average Treatment Effects of Education when Compulsory Schooling Laws Really Matter," American Economic Review, American Economic Association, vol. 96(1), pages 152-175, March.
    11. Angrist, Joshua D & Evans, William N, 1998. "Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size," American Economic Review, American Economic Association, vol. 88(3), pages 450-477, June.
    12. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    13. Philipp Eisenhauer & James J. Heckman & Edward Vytlacil, 2015. "The Generalized Roy Model and the Cost-Benefit Analysis of Social Programs," Journal of Political Economy, University of Chicago Press, vol. 123(2), pages 413-443.
    14. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    15. Sandra E. Black & Paul J. Devereux & Kjell G. Salvanes, 2010. "Small Family, Smart Family? Family Size and the IQ Scores of Young Men," Journal of Human Resources, University of Wisconsin Press, vol. 45(1).
    16. Lance Lochner & Enrico Moretti, 2004. "The Effect of Education on Crime: Evidence from Prison Inmates, Arrests, and Self-Reports," American Economic Review, American Economic Association, vol. 94(1), pages 155-189, March.
    17. Rud, Juan Pablo, 2012. "Electricity provision and industrial development: Evidence from India," Journal of Development Economics, Elsevier, vol. 97(2), pages 352-367.
    18. Christian N. Brinch & Magne Mogstad & Matthew Wiswall, 2017. "Beyond LATE with a Discrete Instrument," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 985-1039.
    19. David Blakeslee & Ram Fishman & Veena Srinivasan, 2020. "Way Down in the Hole: Adaptation to Long-Term Water Loss in Rural India," American Economic Review, American Economic Association, vol. 110(1), pages 200-224, January.
    20. Nicole Maestas & Kathleen J. Mullen & Alexander Strand, 2013. "Does Disability Insurance Receipt Discourage Work? Using Examiner Assignment to Estimate Causal Effects of SSDI Receipt," American Economic Review, American Economic Association, vol. 103(5), pages 1797-1829, August.
    21. Martin Huber & Giovanni Mellace, 2015. "Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 398-411, May.
    22. Lukas Laffers & Giovanni Mellace, 2017. "A note on testing instrument validity for the identification of LATE," Empirical Economics, Springer, vol. 53(3), pages 1281-1286, November.
    23. Taryn Dinkelman, 2011. "The Effects of Rural Electrification on Employment: New Evidence from South Africa," American Economic Review, American Economic Association, vol. 101(7), pages 3078-3108, December.
    24. Magne Mogstad & Alexander Torgovitsky & Christopher R. Walters, 2021. "The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables," American Economic Review, American Economic Association, vol. 111(11), pages 3663-3698, November.
    25. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 555-574.
    26. Sascha Becker & Francesco Cinnirella & Ludger Woessmann, 2010. "The trade-off between fertility and education: evidence from before the demographic transition," Journal of Economic Growth, Springer, vol. 15(3), pages 177-204, September.
    27. Joshua Angrist & Victor Lavy & Analia Schlosser, 2010. "Multiple Experiments for the Causal Link between the Quantity and Quality of Children," Journal of Labor Economics, University of Chicago Press, vol. 28(4), pages 773-824, October.
    28. Felfe, Christina & Lalive, Rafael, 2018. "Does early child care affect children's development?," Journal of Public Economics, Elsevier, vol. 159(C), pages 33-53.
    29. Helmut Farbmacher & Raphael Guber & Sven Klaassen, 2022. "Instrument Validity Tests With Causal Forests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 605-614, April.
    30. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," NBER Working Papers 4483, National Bureau of Economic Research, Inc.
    31. Adriana Lleras-Muney, 2005. "The Relationship Between Education and Adult Mortality in the United States," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 189-221.
    32. Melvin Stephens Jr. & Dou-Yan Yang, 2014. "Compulsory Education and the Benefits of Schooling," American Economic Review, American Economic Association, vol. 104(6), pages 1777-1792, June.
    33. Machado, Cecilia & Shaikh, Azeem M. & Vytlacil, Edward J., 2019. "Instrumental variables and the sign of the average treatment effect," Journal of Econometrics, Elsevier, vol. 212(2), pages 522-555.
    34. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    35. Manudeep Bhuller & Gordon B. Dahl & Katrine V. Løken & Magne Mogstad, 2020. "Incarceration, Recidivism, and Employment," Journal of Political Economy, University of Chicago Press, vol. 128(4), pages 1269-1324.
    36. Pedro Carneiro & James J. Heckman & Edward J. Vytlacil, 2011. "Estimating Marginal Returns to Education," American Economic Review, American Economic Association, vol. 101(6), pages 2754-2781, October.
    37. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    38. Molly Lipscomb & A. Mushfiq Mobarak & Tania Barham, 2013. "Development Effects of Electrification: Evidence from the Topographic Placement of Hydropower Plants in Brazil," American Economic Journal: Applied Economics, American Economic Association, vol. 5(2), pages 200-231, April.
    39. Brigham Frandsen & Lars Lefgren & Emily Leslie, 2023. "Judging Judge Fixed Effects," American Economic Review, American Economic Association, vol. 113(1), pages 253-277, January.
    40. Marshall, John, 2016. "Coarsening Bias: How Coarse Treatment Measurement Upwardly Biases Instrumental Variable Estimates," Political Analysis, Cambridge University Press, vol. 24(2), pages 157-171, April.
    41. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," Working Papers 696, Princeton University, Department of Economics, Industrial Relations Section..
    42. Datta, Saugato, 2012. "The impact of improved highways on Indian firms," Journal of Development Economics, Elsevier, vol. 99(1), pages 46-57.
    43. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
    44. Clément de Chaisemartin, 2017. "Tolerating defiance? Local average treatment effects without monotonicity," Quantitative Economics, Econometric Society, vol. 8(2), pages 367-396, July.
    45. Dalton Conley & Rebecca Glauber, 2006. "Parental Educational Investment and Children’s Academic Risk: Estimates of the Impact of Sibship Size and Birth Order from Exogenous Variation in Fertility," Journal of Human Resources, University of Wisconsin Press, vol. 41(4).
    46. James J. Heckman & John Eric Humphries & Gregory Veramendi, 2018. "Returns to Education: The Causal Effects of Education on Earnings, Health, and Smoking," Journal of Political Economy, University of Chicago Press, vol. 126(S1), pages 197-246.
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