Set identification and sensitivity analysis with Tobin regressors
We give semiparametric identification and estimation results for econometric models with a regressor that is endogenous, bound censored, and selected; it is called a Tobin regressor. First, we show that the true parameter value is set-identified and characterize the identification sets. Second, we p...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
The Econometric Society
2013
|
| Online Access: | http://hdl.handle.net/1721.1/75828 https://orcid.org/0000-0002-9054-3804 https://orcid.org/0000-0003-0395-7177 https://orcid.org/0000-0002-3250-6714 |
| _version_ | 1826199965557325824 |
|---|---|
| author | Chernozhukov, Victor V. Rigobon, Roberto Stoker, Thomas Martin |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Chernozhukov, Victor V. Rigobon, Roberto Stoker, Thomas Martin |
| author_sort | Chernozhukov, Victor V. |
| collection | MIT |
| description | We give semiparametric identification and estimation results for econometric models with a regressor that is endogenous, bound censored, and selected; it is called a Tobin regressor. First, we show that the true parameter value is set-identified and characterize the identification sets. Second, we propose novel estimation and inference methods for this true value. These estimation and inference methods are of independent interest and apply to any problem possessing the sensitivity structure, where the true parameter value is point-identified conditional on some nuisance parameter values that are set-identified. By fixing the nuisance parameter value in some suitable region, we can proceed with regular point and interval estimation. Then we take the union over nuisance parameter values of the point and interval estimates to form the final set estimates and confidence set estimates. The initial point or interval estimates can be frequentist or Bayesian. The final set estimates are set-consistent for the true parameter value, and confidence set estimates have frequentist validity in the sense of covering this value with at least a prespecified probability in large samples. Our procedure may be viewed as a formalization of the sensitivity analysis in the sense of Leamer (1985). We apply our identification, estimation, and inference procedures to study the effects of changes in housing wealth on household consumption. Our set estimates fall in plausible ranges, significantly above low ordinary least squares estimates and below high instrumental variables estimates that do not account for the Tobin regressor structure. |
| first_indexed | 2024-09-23T11:28:38Z |
| format | Article |
| id | mit-1721.1/75828 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:28:38Z |
| publishDate | 2013 |
| publisher | The Econometric Society |
| record_format | dspace |
| spelling | mit-1721.1/758282022-10-01T03:55:41Z Set identification and sensitivity analysis with Tobin regressors Chernozhukov, Victor V. Rigobon, Roberto Stoker, Thomas Martin Massachusetts Institute of Technology. Department of Economics Sloan School of Management Chernozhukov, Victor V. Rigobon, Roberto Stoker, Thomas Martin We give semiparametric identification and estimation results for econometric models with a regressor that is endogenous, bound censored, and selected; it is called a Tobin regressor. First, we show that the true parameter value is set-identified and characterize the identification sets. Second, we propose novel estimation and inference methods for this true value. These estimation and inference methods are of independent interest and apply to any problem possessing the sensitivity structure, where the true parameter value is point-identified conditional on some nuisance parameter values that are set-identified. By fixing the nuisance parameter value in some suitable region, we can proceed with regular point and interval estimation. Then we take the union over nuisance parameter values of the point and interval estimates to form the final set estimates and confidence set estimates. The initial point or interval estimates can be frequentist or Bayesian. The final set estimates are set-consistent for the true parameter value, and confidence set estimates have frequentist validity in the sense of covering this value with at least a prespecified probability in large samples. Our procedure may be viewed as a formalization of the sensitivity analysis in the sense of Leamer (1985). We apply our identification, estimation, and inference procedures to study the effects of changes in housing wealth on household consumption. Our set estimates fall in plausible ranges, significantly above low ordinary least squares estimates and below high instrumental variables estimates that do not account for the Tobin regressor structure. 2013-01-07T18:07:02Z 2013-01-07T18:07:02Z 2010-12 Article http://purl.org/eprint/type/JournalArticle 1759-7323 1759-7331 http://hdl.handle.net/1721.1/75828 Chernozhukov, Victor, Roberto Rigobon, and Thomas M. Stoker. “Set Identification and Sensitivity Analysis with Tobin Regressors.” Quantitative Economics 1.2 (2010): 255–277. https://orcid.org/0000-0002-9054-3804 https://orcid.org/0000-0003-0395-7177 https://orcid.org/0000-0002-3250-6714 en_US http://dx.doi.org/ 10.3982/QE1 Quantitative Economics Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf The Econometric Society MIT web domain |
| spellingShingle | Chernozhukov, Victor V. Rigobon, Roberto Stoker, Thomas Martin Set identification and sensitivity analysis with Tobin regressors |
| title | Set identification and sensitivity analysis with Tobin regressors |
| title_full | Set identification and sensitivity analysis with Tobin regressors |
| title_fullStr | Set identification and sensitivity analysis with Tobin regressors |
| title_full_unstemmed | Set identification and sensitivity analysis with Tobin regressors |
| title_short | Set identification and sensitivity analysis with Tobin regressors |
| title_sort | set identification and sensitivity analysis with tobin regressors |
| url | http://hdl.handle.net/1721.1/75828 https://orcid.org/0000-0002-9054-3804 https://orcid.org/0000-0003-0395-7177 https://orcid.org/0000-0002-3250-6714 |
| work_keys_str_mv | AT chernozhukovvictorv setidentificationandsensitivityanalysiswithtobinregressors AT rigobonroberto setidentificationandsensitivityanalysiswithtobinregressors AT stokerthomasmartin setidentificationandsensitivityanalysiswithtobinregressors |