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This paper proposes to model the conditional distribution of the parameter given the standard errors as a flexibly parameterized location\u2010scale family of distributions, leading to a family of methods that we call\n                    <jats:sc>close<\/jats:sc>\n                    . The\n                    <jats:sc>close<\/jats:sc>\n                    framework unifies and generalizes several proposals under precision dependence. We argue that the most flexible member of the\n                    <jats:sc>close<\/jats:sc>\n                    family is a minimalist and computationally efficient default for accounting for precision dependence. We analyze this method and show that it is competitive in terms of the regret of subsequent decision rules. Empirically, using\n                    <jats:sc>close<\/jats:sc>\n                    leads to sizable gains for selecting high\u2010mobility Census tracts.\n                  <\/jats:p>","DOI":"10.3982\/ecta22935","type":"journal-article","created":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T06:11:56Z","timestamp":1774591916000},"page":"305-340","source":"Crossref","is-referenced-by-count":3,"title":["Empirical Bayes When Estimation Precision Predicts Parameters"],"prefix":"10.3982","volume":"94","author":[{"given":"Jiafeng","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Economics, Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2026]]},"reference":[{"key":"ecta70008-bib-0001","unstructured":"Abadie, Alberto, Anish Agarwal, Guido Imbens, Siwei Jia, James McQueen, and Serguei Stepaniants (2023), \u201cEstimating the Value of Evidence-Based Decision Making.\u201d arXiv:2306.13681. arXiv preprint."},{"key":"ecta70008-bib-0002","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.1093\/qje\/qjab017","volume":"136","author":"Abaluck","year":"2021","journal-title":"The Quarterly Journal of Economics"},{"key":"ecta70008-bib-0003","unstructured":"Aloni, Tslil and Hadar Avivi (2023), \u201cOne Land, Many Promises: the Unequal Consequences of Childhood Location for Natives and Immigrants in Israel.\u201d"},{"key":"ecta70008-bib-0004","doi-asserted-by":"crossref","first-page":"2766","DOI":"10.1257\/aer.20180310","volume":"109","author":"Andrews","year":"2019","journal-title":"American Economic Review"},{"key":"ecta70008-bib-0005","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1093\/qje\/qjad043","volume":"139","author":"Andrews","year":"2024","journal-title":"The Quarterly Journal of Economics"},{"key":"ecta70008-bib-0006","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1093\/qje\/qjx001","volume":"132","author":"Angrist","year":"2017","journal-title":"The Quarterly Journal of Economics"},{"key":"ecta70008-bib-0007","doi-asserted-by":"crossref","first-page":"489","DOI":"10.3982\/ECTA6895","volume":"77","author":"Arellano","year":"2009","journal-title":"Econometrica"},{"key":"ecta70008-bib-0008","doi-asserted-by":"crossref","first-page":"655","DOI":"10.3982\/ECTA14434","volume":"86","author":"Armstrong","year":"2018","journal-title":"Econometrica"},{"key":"ecta70008-bib-0009","doi-asserted-by":"crossref","first-page":"2567","DOI":"10.3982\/ECTA18597","volume":"90","author":"Armstrong","year":"2022","journal-title":"Econometrica"},{"key":"ecta70008-bib-0010","doi-asserted-by":"crossref","first-page":"2992","DOI":"10.1257\/aer.20201653","volume":"112","author":"Arnold","year":"2022","journal-title":"American Economic Review"},{"key":"ecta70008-bib-0011","doi-asserted-by":"crossref","first-page":"133","DOI":"10.3982\/ECTA15732","volume":"89","author":"Athey","year":"2021","journal-title":"Econometrica"},{"key":"ecta70008-bib-0012","first-page":"608","volume":"35(2)","author":"Audibert","year":"2007","journal-title":"Annals of Statistics"},{"key":"ecta70008-bib-0013","doi-asserted-by":"crossref","first-page":"4614","DOI":"10.1086\/710607","volume":"128","author":"Azevedo","year":"2020","journal-title":"Journal of Political Economy"},{"key":"ecta70008-bib-0014","doi-asserted-by":"crossref","first-page":"1897","DOI":"10.1086\/728110","volume":"132","author":"Baum-Snow","year":"2024","journal-title":"Journal of Political Economy"},{"key":"ecta70008-bib-0015","doi-asserted-by":"crossref","first-page":"1281","DOI":"10.1257\/aer.20200407","volume":"114","author":"Bergman","year":"2024","journal-title":"American Economic Review"},{"key":"ecta70008-bib-0016","first-page":"209","volume":"3(1)","author":"Bock","year":"1975","journal-title":"The Annals of Statistics"},{"key":"ecta70008-bib-0017","doi-asserted-by":"crossref","unstructured":"Bonhomme, St\u00e9phane and Angela Denis (2024), \u201cFixed Effects and Beyond: Bias Reduction, Groups, Shrinkage, and Factors in Panel Data.\u201d Tech. rep.","DOI":"10.53479\/40051"},{"key":"ecta70008-bib-0018","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.3982\/ECTA11319","volume":"83","author":"Bonhomme","year":"2015","journal-title":"Econometrica"},{"key":"ecta70008-bib-0019","doi-asserted-by":"crossref","unstructured":"Bonhomme, St\u00e9phane, Kerstin Holzheu, Thibaut Lamadon, Elena Manresa, Magne Mogstad, and Bradley Setzler (2020), \u201cHow Much Should We Trust Estimates of Firm Effects and Worker Sorting?\u201d","DOI":"10.3386\/w27368"},{"key":"ecta70008-bib-0020","unstructured":"Bonvini, Matteo, Edward H. 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