Unbiased instrumental variables estimation under known first-stage sign
We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first-stage coefficients is known. In the case with a single instrument, there is a unique nonrandomized unbiased estimator based on the r...
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| Other Authors: | |
| Format: | Article |
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The Econometric Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/113709 |
| _version_ | 1826204234180198400 |
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| author | Armstrong, Timothy B. Andrews, Isaiah Smith |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Armstrong, Timothy B. Andrews, Isaiah Smith |
| author_sort | Armstrong, Timothy B. |
| collection | MIT |
| description | We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first-stage coefficients is known. In the case with a single instrument, there is a unique nonrandomized unbiased estimator based on the reduced-form and first-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the two-stage least squares estimator. Our finite-sample results apply to normal models with known variance for the reduced-form errors, and imply analogous results under weak-instrument asymptotics with an unknown error distribution. Keyword: unbiased estimation; weak instruments |
| first_indexed | 2024-09-23T12:51:02Z |
| format | Article |
| id | mit-1721.1/113709 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T12:51:02Z |
| publishDate | 2018 |
| publisher | The Econometric Society |
| record_format | dspace |
| spelling | mit-1721.1/1137092022-09-28T10:27:46Z Unbiased instrumental variables estimation under known first-stage sign Armstrong, Timothy B. Andrews, Isaiah Smith Massachusetts Institute of Technology. Department of Economics Andrews, Isaiah Smith We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first-stage coefficients is known. In the case with a single instrument, there is a unique nonrandomized unbiased estimator based on the reduced-form and first-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the two-stage least squares estimator. Our finite-sample results apply to normal models with known variance for the reduced-form errors, and imply analogous results under weak-instrument asymptotics with an unknown error distribution. Keyword: unbiased estimation; weak instruments 2018-02-16T16:39:22Z 2018-02-16T16:39:22Z 2017-07 2016-04 2018-02-13T17:59:55Z Article http://purl.org/eprint/type/JournalArticle 1759-7323 1759-7331 http://hdl.handle.net/1721.1/113709 Andrews, Isaiah, and Armstrong, Timothy B. “Unbiased Instrumental Variables Estimation Under Known First-Stage Sign.” Quantitative Economics 8, 2 (July 2017): 479–503 © 2017 The Authors http://dx.doi.org/10.3982/QE700 Quantitative Economics Creative Commons Attribution-NonCommercial 4.0 International http://creativecommons.org/licenses/by-nc/4.0/ application/pdf The Econometric Society Wiley |
| spellingShingle | Armstrong, Timothy B. Andrews, Isaiah Smith Unbiased instrumental variables estimation under known first-stage sign |
| title | Unbiased instrumental variables estimation under known first-stage sign |
| title_full | Unbiased instrumental variables estimation under known first-stage sign |
| title_fullStr | Unbiased instrumental variables estimation under known first-stage sign |
| title_full_unstemmed | Unbiased instrumental variables estimation under known first-stage sign |
| title_short | Unbiased instrumental variables estimation under known first-stage sign |
| title_sort | unbiased instrumental variables estimation under known first stage sign |
| url | http://hdl.handle.net/1721.1/113709 |
| work_keys_str_mv | AT armstrongtimothyb unbiasedinstrumentalvariablesestimationunderknownfirststagesign AT andrewsisaiahsmith unbiasedinstrumentalvariablesestimationunderknownfirststagesign |