Tests with correct size when instruments can be arbitrarily weak

Moreira, Marcelo J.

doi:10.1016/j.jeconom.2009.01.012

“…The critical values suggest that the bias of IV estimates for some small subgroups in our sample such as men or specific age cohorts is likely to be sometimes above 25 percent when we analyze heterogeneity in the migration effect. We follow Moreira (2003), Moreira (2009) and Mikusheva and Poi (2006a) by using the conditional likelihood ratio (CLR) test, which is valid under weak instruments, to ascertain whether the migration effect is significantly different from zero and positive or negative, where possible. We also calculate the CLR confidence region for the migration coefficient (Andrews et al (2006) implemented in STATA using a package provided by Mikusheva and Poi (2006a)).…”

Section: Identification Strategymentioning

confidence: 99%

Alone but better off? Adult child migration and health of elderly parents in Moldova

Böhme

¹

,

Persian²,

Stöhr

³

2015

Journal of Health Economics

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractIncreasing labor migration and simultaneous aging of societies are two important demographic developments many poor countries face. Elderly people who are left behind may experience a decrease in welfare when their children migrate. This paper investigates the effect of migration on various dimensions of elderly health using unique data from Moldova, which has one of the highest emigration rates in the world. We find positive migration effects on the body mass index (BMI), mobility and self-reported health. No effects are found on depression and cognitive capacity. We trace these positive outcomes to an income effect which leads to improvements in diet and a reallocation of time use from subsistence farming to leisure and sleep. These positive effects seem to compensate the elderly for decreasing social contact with their migrant family members.

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“…We can prove this result directly from Theorem 2-(a) of Moreira (2001Moreira ( , 2009 for homoskedastic errors (with the scalar µ and matrix Ω being replaced by µ Φ and Σ). As this setup resembles the just-identified model with homoskedastic errors, optimality of the Anderson-Rubin test for HAC errors and k = 1 follows straightforwardly.…”

Section: Proposition 3 a Test Is Said To Be Locally Unbiased (Lu) Ifmentioning

confidence: 93%

Optimal Two-Sided Tests for Instrumental Variables Regression with Heteroskedastic and Autocorrelated Errors

Moreira

¹

,

Moreira

²

2015

Self Cite

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1 This paper expands upon and supersedes the corresponding sections of our working paper "Contributions to the Theory of Optimal Tests." We thank Benjamin Mills and Gustavo de Castro for outstanding research assistance, and are particularly indebted to Gustavo for suggesting and implementing the designs for power comparisons reported here. We thank Leandro Gorno, Patrik Guggenberger, Alexei Onatski, and Lucas Vilela for helpful comments; Jose Diogo Barbosa, Felipe Flores, and Leonardo Salim for suggestions on earlier drafts of this paper; and Isaiah Andrews and Jose Olea for productive discussions and sharing numerical codes. We gratefully acknowledge the research support of CNPq, FAPERJ, and NSF (via grant SES-0819761). arXiv:1505.06644v1 [math.ST] 25 May 2015Abstract This paper considers two-sided tests for the parameter of an endogenous variable in an instrumental variable (IV) model with heteroskedastic and autocorrelated errors. We develop the finite-sample theory of weighted-average power (WAP) tests with normal errors and a known long-run variance. We introduce two weights which are invariant to orthogonal transformations of the instruments; e.g., changing the order in which the instruments appear. While tests using the MM1 weight can be severely biased, optimal tests based on the MM2 weight are naturally two-sided when errors are homoskedastic.We propose two boundary conditions that yield two-sided tests whether errors are homoskedastic or not. The locally unbiased (LU) condition is related to the power around the null hypothesis and is a weaker requirement than unbiasedness. The strongly unbiased (SU) condition is more restrictive than LU, but the associated WAP tests are easier to implement. Several tests are SU in finite samples or asymptotically, including tests robust to weak IV (such as the Anderson-Rubin, score, conditional quasi-likelihood ratio, and I. Andrews' (2015) PI-CLC tests) and two-sided tests which are optimal when the sample size is large and instruments are strong.We refer to the WAP-SU tests based on our weights as MM1-SU and MM2-SU tests. Dropping the restrictive assumptions of normality and known variance, the theory is shown to remain valid at the cost of asymptotic approximations. The MM2-SU test is optimal under the strong IV asymptotics, and outperforms other existing tests under the weak IV asymptotics.

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“…Kleibergen (2006) instead adapts the formula for the likelihood ratio statistic derived by Moreira (2003) in the homoskedastic IV model to the GMM framework. For the HAC-IV model, this quasi likelihood ratio statistic becomes…”

Section: The IV Model and Statisticsmentioning

confidence: 99%

Nonparametric analysis of random utility models

Moreira

¹

,

Moreira

²

2016

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1 This paper expands upon and supersedes the corresponding sections of our working paper "Contributions to the Theory of Optimal Tests." We thank Benjamin Mills and Gustavo de Castro for outstanding research assistance, and are particularly indebted to Gustavo for suggesting and implementing the designs for power comparisons reported here. We thank Leandro Gorno, Patrik Guggenberger, Alexei Onatski, and Lucas Vilela for helpful comments; Jose Diogo Barbosa, Felipe Flores, and Leonardo Salim for suggestions on earlier drafts of this paper; and Isaiah Andrews and Jose Olea for productive discussions and sharing numerical codes. We gratefully acknowledge the research support of CNPq, FAPERJ, and NSF (via grant SES-0819761). arXiv:1505.06644v1 [math.ST] 25 May 2015Abstract This paper considers two-sided tests for the parameter of an endogenous variable in an instrumental variable (IV) model with heteroskedastic and autocorrelated errors. We develop the finite-sample theory of weighted-average power (WAP) tests with normal errors and a known long-run variance. We introduce two weights which are invariant to orthogonal transformations of the instruments; e.g., changing the order in which the instruments appear. While tests using the MM1 weight can be severely biased, optimal tests based on the MM2 weight are naturally two-sided when errors are homoskedastic.We propose two boundary conditions that yield two-sided tests whether errors are homoskedastic or not. The locally unbiased (LU) condition is related to the power around the null hypothesis and is a weaker requirement than unbiasedness. The strongly unbiased (SU) condition is more restrictive than LU, but the associated WAP tests are easier to implement. Several tests are SU in finite samples or asymptotically, including tests robust to weak IV (such as the Anderson-Rubin, score, conditional quasi-likelihood ratio, and I. Andrews' (2015) PI-CLC tests) and two-sided tests which are optimal when the sample size is large and instruments are strong.We refer to the WAP-SU tests based on our weights as MM1-SU and MM2-SU tests. Dropping the restrictive assumptions of normality and known variance, the theory is shown to remain valid at the cost of asymptotic approximations. The MM2-SU test is optimal under the strong IV asymptotics, and outperforms other existing tests under the weak IV asymptotics.

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Tests with correct size when instruments can be arbitrarily weak

Cited by 155 publications

References 17 publications

Alone but better off? Adult child migration and health of elderly parents in Moldova

Alone but better off? Adult child migration and health of elderly parents in Moldova

Optimal Two-Sided Tests for Instrumental Variables Regression with Heteroskedastic and Autocorrelated Errors

Nonparametric analysis of random utility models

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