Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis
© 2020 The Econometric Society Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researcher...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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The Econometric Society
2021
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| Online Access: | https://hdl.handle.net/1721.1/136224 |
| _version_ | 1826205764859985920 |
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| author | Abadie, Alberto Athey, Susan Imbens, Guido W Wooldridge, Jeffrey M |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Abadie, Alberto Athey, Susan Imbens, Guido W Wooldridge, Jeffrey M |
| author_sort | Abadie, Alberto |
| collection | MIT |
| description | © 2020 The Econometric Society Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of interest and report standard errors that are designed to capture sampling variation. This is common even in applications where it is difficult to articulate what that population of interest is, and how it differs from the sample. In this article, we explore an alternative approach to inference, which is partly design-based. In a design-based setting, the values of some of the regressors can be manipulated, perhaps through a policy intervention. Design-based uncertainty emanates from lack of knowledge about the values that the regression outcome would have taken under alternative interventions. We derive standard errors that account for design-based uncertainty instead of, or in addition to, sampling-based uncertainty. We show that our standard errors in general are smaller than the usual infinite-population sampling-based standard errors and provide conditions under which they coincide. |
| first_indexed | 2024-09-23T13:18:40Z |
| format | Article |
| id | mit-1721.1/136224 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:18:40Z |
| publishDate | 2021 |
| publisher | The Econometric Society |
| record_format | dspace |
| spelling | mit-1721.1/1362242023-09-14T19:46:24Z Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis Abadie, Alberto Athey, Susan Imbens, Guido W Wooldridge, Jeffrey M Massachusetts Institute of Technology. Department of Economics © 2020 The Econometric Society Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of interest and report standard errors that are designed to capture sampling variation. This is common even in applications where it is difficult to articulate what that population of interest is, and how it differs from the sample. In this article, we explore an alternative approach to inference, which is partly design-based. In a design-based setting, the values of some of the regressors can be manipulated, perhaps through a policy intervention. Design-based uncertainty emanates from lack of knowledge about the values that the regression outcome would have taken under alternative interventions. We derive standard errors that account for design-based uncertainty instead of, or in addition to, sampling-based uncertainty. We show that our standard errors in general are smaller than the usual infinite-population sampling-based standard errors and provide conditions under which they coincide. 2021-10-27T20:34:20Z 2021-10-27T20:34:20Z 2020 2021-03-25T16:41:04Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136224 en 10.3982/ECTA12675 Econometrica Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf The Econometric Society arXiv |
| spellingShingle | Abadie, Alberto Athey, Susan Imbens, Guido W Wooldridge, Jeffrey M Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis |
| title | Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis |
| title_full | Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis |
| title_fullStr | Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis |
| title_full_unstemmed | Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis |
| title_short | Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis |
| title_sort | sampling based versus design based uncertainty in regression analysis |
| url | https://hdl.handle.net/1721.1/136224 |
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