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Identification- and Singularity-Robust Inference for Moment Condition

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This paper introduces two new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) test and a new identi?cation- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2 + gamma bounded moments for some gamma > 0: No conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions. The SR-CQLR test is shown to be asymptotically e?icient in a GMM sense under strong and semi-strong identi?cation (for all k greater than or equal to p; where k and p are the numbers of moment conditions and parameters, respectively). The SR-CQLR test reduces asymptotically to Moreira’s CLR test when p = 1 in the homoskedastic linear IV model. The same is true for p greater than or equal to 2 in most, but not all, identi?cation scenarios. We also introduce versions of the SR-CQLR and SR-AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identi?ed. The subvector SR-CQLR test is shown to be asymptotically e?icient in a GMM sense under strong and semi-strong identi?cation.

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  • Donald W. K. Andrews & Patrik Guggenberger, 2015. "Identification- and Singularity-Robust Inference for Moment Condition," Cowles Foundation Discussion Papers 1978R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2018.
  • Handle: RePEc:cwl:cwldpp:1978r
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    1. Jin Seo Cho & Halbert White, 2007. "Testing for Regime Switching," Econometrica, Econometric Society, vol. 75(6), pages 1671-1720, November.
    2. Canova, Fabio & Sala, Luca, 2009. "Back to square one: Identification issues in DSGE models," Journal of Monetary Economics, Elsevier, vol. 56(4), pages 431-449, May.
    3. Christopher D. Carroll & Jiri Slacalek & Martin Sommer, 2011. "International Evidence on Sticky Consumption Growth," The Review of Economics and Statistics, MIT Press, vol. 93(4), pages 1135-1145, November.
    4. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    5. Zhongjun Qu & Denis Tkachenko, 2012. "Identification and frequency domain quasi‐maximum likelihood estimation of linearized dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 3(1), pages 95-132, March.
    6. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    7. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    8. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    9. Patrik Guggenberger & Frank Kleibergen & Sophocles Mavroeidis & Linchun Chen, 2012. "On the Asymptotic Sizes of Subset Anderson–Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression," Econometrica, Econometric Society, vol. 80(6), pages 2649-2666, November.
    10. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    11. Puhani, Patrick A, 2000. " The Heckman Correction for Sample Selection and Its Critique," Journal of Economic Surveys, Wiley Blackwell, vol. 14(1), pages 53-68, February.
    12. Nicky Grant, 2013. "Identification Robust Inference with Singular Variance," The School of Economics Discussion Paper Series 1315, Economics, The University of Manchester.
    13. Gomes, Fábio Augusto Reis & Paz, Lourenço S., 2013. "Estimating the elasticity of intertemporal substitution: Is the aggregate financial return free from the weak instrument problem?," Journal of Macroeconomics, Elsevier, vol. 36(C), pages 63-75.
    14. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Admissible Invariant Similar Tests For Instrumental Variables Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 806-818, June.
    15. Choi, In & Phillips, Peter C. B., 1992. "Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 113-150.
    16. Whitney K. Newey & Frank Windmeijer, 2009. "Generalized Method of Moments With Many Weak Moment Conditions," Econometrica, Econometric Society, vol. 77(3), pages 687-719, May.
    17. repec:eee:econom:v:200:y:2017:i:1:p:17-35 is not listed on IDEAS
    18. Luiz M. Cruz & Marcelo J. Moreira, 2005. "On the Validity of Econometric Techniques with Weak Instruments: Inference on Returns to Education Using Compulsory School Attendance Laws," Journal of Human Resources, University of Wisconsin Press, vol. 40(2).
    19. Chaudhuri, Saraswata & Zivot, Eric, 2011. "A new method of projection-based inference in GMM with weakly identified nuisance parameters," Journal of Econometrics, Elsevier, vol. 164(2), pages 239-251, October.
    20. Timothy B. Armstrong, 2016. "Large Market Asymptotics for Differentiated Product Demand Estimators With Economic Models of Supply," Econometrica, Econometric Society, vol. 84, pages 1961-1980, September.
    21. Dufour, Jean-Marie & Jasiak, Joann, 2001. "Finite Sample Limited Information Inference Methods for Structural Equations and Models with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 815-843, August.
    22. Kleibergen, Frank & Mavroeidis, Sophocles, 2009. "Weak Instrument Robust Tests in GMM and the New Keynesian Phillips Curve," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 293-311.
    23. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    24. Guggenberger, Patrik, 2012. "On The Asymptotic Size Distortion Of Tests When Instruments Locally Violate The Exogeneity Assumption," Econometric Theory, Cambridge University Press, vol. 28(2), pages 387-421, April.
    25. Nelson, Charles R. & Startz, Richard, 2007. "The zero-information-limit condition and spurious inference in weakly identified models," Journal of Econometrics, Elsevier, vol. 138(1), pages 47-62, May.
    26. Frank Kleibergen, 2004. "Testing Subsets of Structural Parameters in the Instrumental Variables," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 418-423, February.
    27. Hillier, Grant, 2009. "Exact Properties Of The Conditional Likelihood Ratio Test In An Iv Regression Model," Econometric Theory, Cambridge University Press, vol. 25(04), pages 915-957, August.
    28. Chaudhuri, Saraswata & Richardson, Thomas & Robins, James & Zivot, Eric, 2010. "A New Projection-Type Split-Sample Score Test In Linear Instrumental Variables Regression," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1820-1837, December.
    29. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
    30. Chen, Xiaohong & Ponomareva, Maria & Tamer, Elie, 2014. "Likelihood inference in some finite mixture models," Journal of Econometrics, Elsevier, vol. 182(1), pages 87-99.
    31. Neely, Christopher J & Roy, Amlan & Whiteman, Charles H, 2001. "Risk Aversion versus Intertemporal Substitution: A Case Study of Identification Failure in the Intertemporal Consumption Capital Asset Pricing Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 395-403, October.
    32. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(5), pages 1131-1147, October.
    33. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July.
    34. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
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    More about this item

    Keywords

    Asymptotics; Conditional likelihood ratio test; Confidence set; Identification; Inference; Moment conditions; Robust; Singular variance; Test; Weak identification; Weak instruments;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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