ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS
This paper derives the limiting distributions of alternative jackknife instrumental variables (JIV) estimators and gives formulas for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of...
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Cambridge University Press
2013
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| Online Access: | http://hdl.handle.net/1721.1/82651 https://orcid.org/0000-0003-2699-4704 https://orcid.org/0000-0002-5433-9435 |
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| author | Chao, John C. Swanson, Norman R. Hausman, Jerry A. Newey, Whitney K. Woutersen, Tiemen |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Chao, John C. Swanson, Norman R. Hausman, Jerry A. Newey, Whitney K. Woutersen, Tiemen |
| author_sort | Chao, John C. |
| collection | MIT |
| description | This paper derives the limiting distributions of alternative jackknife instrumental variables (JIV) estimators and gives formulas for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of Bekker (1994, Econometrica 62, 657–681) and the many weak instrument sequence of Chao and Swanson (2005, Econometrica 73, 1673–1691). We show that JIV estimators are asymptotically normal and that standard errors are consistent provided that as n→∞, where K[subscript n] and r[subscript n] denote, respectively, the number of instruments and the concentration parameter. This is in contrast to the asymptotic behavior of such classical instrumental variables estimators as limited information maximum likelihood, bias-corrected two-stage least squares, and two-stage least squares, all of which are inconsistent in the presence of heteroskedasticity, unless K[subscript n]/r[subscript n]→0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on the strength of the instruments as measured by the relative orders of magnitude of r[subscript n] and K[subscript n]. |
| first_indexed | 2024-09-23T10:05:41Z |
| format | Article |
| id | mit-1721.1/82651 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:05:41Z |
| publishDate | 2013 |
| publisher | Cambridge University Press |
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| spelling | mit-1721.1/826512022-09-30T18:52:40Z ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS Chao, John C. Swanson, Norman R. Hausman, Jerry A. Newey, Whitney K. Woutersen, Tiemen Massachusetts Institute of Technology. Department of Economics Hausman, Jerry A. Newey, Whitney K. This paper derives the limiting distributions of alternative jackknife instrumental variables (JIV) estimators and gives formulas for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of Bekker (1994, Econometrica 62, 657–681) and the many weak instrument sequence of Chao and Swanson (2005, Econometrica 73, 1673–1691). We show that JIV estimators are asymptotically normal and that standard errors are consistent provided that as n→∞, where K[subscript n] and r[subscript n] denote, respectively, the number of instruments and the concentration parameter. This is in contrast to the asymptotic behavior of such classical instrumental variables estimators as limited information maximum likelihood, bias-corrected two-stage least squares, and two-stage least squares, all of which are inconsistent in the presence of heteroskedasticity, unless K[subscript n]/r[subscript n]→0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on the strength of the instruments as measured by the relative orders of magnitude of r[subscript n] and K[subscript n]. 2013-12-06T13:29:06Z 2013-12-06T13:29:06Z 2011-09 Article http://purl.org/eprint/type/JournalArticle 0266-4666 1469-4360 http://hdl.handle.net/1721.1/82651 Chao, John C., Norman R. Swanson, Jerry A. Hausman, Whitney K. Newey, and Tiemen Woutersen. “ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS.” Econometric Theory 28, no. 01 (February 13, 2012): 42-86. © Cambridge University Press 2011 https://orcid.org/0000-0003-2699-4704 https://orcid.org/0000-0002-5433-9435 en_US http://dx.doi.org/10.1017/s0266466611000120 Econometric Theory Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Cambridge University Press Other univ. web domain |
| spellingShingle | Chao, John C. Swanson, Norman R. Hausman, Jerry A. Newey, Whitney K. Woutersen, Tiemen ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS |
| title | ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS |
| title_full | ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS |
| title_fullStr | ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS |
| title_full_unstemmed | ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS |
| title_short | ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS |
| title_sort | asymptotic distribution of jive in a heteroskedastic iv regression with many instruments |
| url | http://hdl.handle.net/1721.1/82651 https://orcid.org/0000-0003-2699-4704 https://orcid.org/0000-0002-5433-9435 |
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