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Testing Missing at Random using Instrumental Variables

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  • Christoph Breunig

Abstract

This paper proposes a test for missing at random (MAR). The MAR assumption is shown to be testable given instrumental variables which are independent of response given potential outcomes. A nonparametric testing procedure based on integrated squared distance is proposed. The statistic’s asymptotic distribu- tion under the MAR hypothesis is derived. We demonstrate that our results can be easily extended to a test of missing completely at random (MCAR) and miss- ing completely at random conditional on covariates X (MCAR(X)). A Monte Carlo study examines finite sample performance of our test statistic. An empirical illustration concerns pocket prescription drug spending with missing values; we reject MCAR but fail to reject MAR.

Suggested Citation

  • Christoph Breunig, 2015. "Testing Missing at Random using Instrumental Variables," SFB 649 Discussion Papers SFB649DP2015-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2015-016
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    References listed on IDEAS

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    1. Armstrong, Timothy B., 2015. "Asymptotically exact inference in conditional moment inequality models," Journal of Econometrics, Elsevier, vol. 186(1), pages 51-65.
    2. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
    3. Patrick Kline & Andres Santos, 2013. "Sensitivity to missing data assumptions: Theory and an evaluation of the U.S. wage structure," Quantitative Economics, Econometric Society, vol. 4(2), pages 231-267, July.
    4. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    5. Richard Blundell & Joel L. Horowitz, 2007. "A Non-Parametric Test of Exogeneity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1035-1058.
    6. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    7. Feve, Frederique & Florens, Jean-Pierre & Van Keilegom, Ingrid, 2012. "Estimation of conditional ranks and tests of exogeneity in nonparametric nonseparable models," LIDAM Discussion Papers ISBA 2012036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    9. Annie Qu, 2002. "Testing ignorable missingness in estimating equation approaches for longitudinal data," Biometrika, Biometrika Trust, vol. 89(4), pages 841-850, December.
    10. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    11. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    12. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    13. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    14. Breunig, Christoph, 2015. "Goodness-of-fit tests based on series estimators in nonparametric instrumental regression," Journal of Econometrics, Elsevier, vol. 184(2), pages 328-346.
    15. Esmeralda A. Ramalho & Richard J. Smith, 2013. "Discrete Choice Non-Response," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(1), pages 343-364.
    16. Kung‐Yee Liang & Jing Qin, 2000. "Regression analysis under non‐standard situations: a pairwise pseudolikelihood approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 773-786.
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    Cited by:

    1. Breunig, Christoph & Kummer, Michael & Ohnemus, Jörg & Viete, Steffen, 2016. "IT outsourcing and firm productivity: Eliminating bias from selective missingness in the dependent variable," ZEW Discussion Papers 16-092, ZEW - Leibniz Centre for European Economic Research.

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    More about this item

    Keywords

    Incomplete data; missing-data mechanism; selection model; nonparametric hypothesis testing; consistent testing; instrumental variable; series estimation.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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