×

zbMATH — the first resource for mathematics

Testing under weak identification with conditional moment restrictions. (English) Zbl 1281.62114
Summary: We propose a semiparametric test for the value of coefficients in models with conditional moment restrictions that has correct size regardless of identification strength. The test is in essence an Anderson-Rubin (AR) test using nonparametrically estimated instruments to which we apply a standard error correction. We show that the test is (1) always size-correct, (2) consistent when identification is not too weak, and (3) asymptotically equivalent to an infeasible AR test when identification is sufficiently strong. We moreover prove that under homoskedasticity and strong identification our test has a limiting noncentral chi-square distribution under a sequence of local alternatives, where the noncentrality parameter is given by a quadratic form of the inverse of the semiparametric efficiency bound.

MSC:
62G10 Nonparametric hypothesis testing
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Many Weak Moment Asymptotics for the Continuously Updated GMM Estimator (2004)
[2] DOI: 10.3982/ECTA6224 · Zbl 1176.62055
[3] DOI: 10.2307/2938351 · Zbl 0728.62107
[4] DOI: 10.1111/1468-0262.00438 · Zbl 1151.62367
[5] DOI: 10.1111/j.1468-0262.2005.00610.x · Zbl 1152.91715
[6] DOI: 10.2307/2171740 · Zbl 0886.62116
[7] DOI: 10.1111/1468-0262.00353 · Zbl 1141.62361
[8] DOI: 10.1111/j.1468-0262.2004.00545.x · Zbl 1141.91635
[9] DOI: 10.1016/j.jeconom.2009.02.005 · Zbl 1431.62188
[10] DOI: 10.1214/aop/1022677271 · Zbl 0942.60004
[11] DOI: 10.2307/1909757 · Zbl 0382.62095
[12] Stochastic Limit Theory (1994)
[13] Instrumental Variable Estimation with Heterskedasticity and Many Instruments (2007)
[14] DOI: 10.1111/j.1468-0262.2005.00632.x · Zbl 1151.62366
[15] DOI: 10.1111/j.1468-0262.2006.00652.x · Zbl 1112.62136
[16] DOI: 10.2307/2951662 · Zbl 0795.62102
[17] DOI: 10.1111/j.1468-0262.2006.00680.x · Zbl 1128.62022
[18] DOI: 10.1214/aoms/1177730090 · Zbl 0033.08002
[19] Asymptotic Statistics (1998) · Zbl 0910.62001
[20] DOI: 10.1214/aos/1176343886 · Zbl 0366.62051
[21] Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg pp 109– (2005)
[22] DOI: 10.1198/073500102288618658
[23] DOI: 10.1111/1468-0262.00151 · Zbl 1015.62105
[24] DOI: 10.2307/2171753 · Zbl 0871.62101
[25] DOI: 10.2307/1911033 · Zbl 0651.62107
[26] DOI: 10.1017/S0266466600012408
[27] Efficient Estimation of Models with Conditional Moment Restrictions pp 419– (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.