A Practitioner’s Guide to Cluster-Robust Inference
Abstract
We consider statistical inference for regression when data are grouped into clusters, with regression model errors independent across clusters but correlated within clusters. Examples include data on individuals with clustering on village or region or other category such as industry, and state-year differences-in-differences studies with clustering on state. In such settings default standard errors can greatly overstate estimator precision. Instead, if the number of clusters is large, statistical inference after OLS should be based on cluster-robust standard errors. We outline the basic method as well as many complications that can arise in practice. These include cluster-specific fixed efects, few clusters, multi-way clustering, and estimators other than OLS.
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Using robust (White) standard errors to compute 90% Wald confidence intervals ensures valid inference even when certain model assumptions are violated.
“This type of standard errors ensures valid inference even when certain model assumptions are violated.”
From Play Favorites: A Statistical Method to Measure Self-Bias in LLM-as-a-Judge (2025) · cites this paper as Cameron and Miller, 2015
The Introduction (p. 2) says cluster-robust standard errors can accommodate within-cluster error correlation without specifying its form, but require the number of clusters to grow. The Empirical Example (pp. 40–41) shows that ordinary White heteroskedastic-robust standard errors can substantially understate uncertainty when errors are clustered. The paper therefore does not support an unqualified assurance that White standard errors ensure valid 90% Wald confidence intervals whenever model assumptions are violated. (LLM, conf=0.87)
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An Introductory Guide to Event Study Models
Miller, D. L. (2023) · Journal of Economic Perspectives · doi:10.1257/jep.37.2.203 · Cited by 360 · see citing works
Self-citationFrom periphery to core: measuring agglomeration effects using high-speed rail
Ahlfeldt, G. M., & Feddersen, A. (2017) · Journal of Economic Geography · doi:10.1093/jeg/lbx005 · Cited by 356 · see citing works
On doing relevant and rigorous experiments: Review and recommendations
Lonati, S., Quiroga, B. F., Zehnder, C., & Antonakis, J. (2018) · Journal of Operations Management · doi:10.1016/j.jom.2018.10.003 · Cited by 359 · see citing works
Gong, J., Wang, G., Wang, Y., Chen, X., Chen, Y., Meng, Q., Yang, P., Yao, Y., & Zhao, Y. (2022) · The Lancet Public Health · doi:10.1016/s2468-2667(22)00203-1 · Cited by 352 · see citing works
Public R&D Investments and Private-sector Patenting: Evidence from NIH Funding Rules
Azoulay, P., Graff Zivin, J. S., Li, D., & Sampat, B. N. (2019) · The Review of Economic Studies · doi:10.1093/restud/rdy034 · Cited by 349 · see citing works
Gender Differences in the Choice of Major: The Importance of Female Role Models
Porter, C., & Serra, D. (2020) · American Economic Journal Applied Economics · doi:10.1257/app.20180426 · Cited by 349 · see citing works
Institutional investors and corporate social responsibility
Nofsinger, J. R., Sulaeman, J., & Varma, A. (2019) · Journal of Corporate Finance · doi:10.1016/j.jcorpfin.2019.07.012 · Cited by 353 · see citing works
Flexible Wages, Bargaining, and the Gender Gap
Biasi, B., & Sarsons, H. (2021) · The Quarterly Journal of Economics · doi:10.1093/qje/qjab026 · Cited by 338 · see citing works
Knocking on Tax Haven’s Door: Multinational Firms and Transfer Pricing
Davies, R. B., Martin, J., Parenti, M., & Farid Toubal, B. (2017) · The Review of Economics and Statistics · doi:10.1162/rest_a_00673 · Cited by 328 · see citing works
Farm production, market access and dietary diversity in Malawi
Koppmair, S., Kassie, M., & Qaim, M. (2017) · Public Health Nutrition · doi:10.1017/s1368980016002135 · Cited by 389 · see citing works
Inference in Regression Discontinuity Designs with a Discrete Running Variable
Kolesár, M., & Rothe, C. (2018) · American Economic Review · doi:10.1257/aer.20160945 · Cited by 326 · see citing works
COVID ‐19 and the Demand for Online Food Shopping Services: Empirical Evidence from Taiwan
Chang, H., & Meyerhoefer, C. D. (2020) · American Journal of Agricultural Economics · doi:10.1111/ajae.12170 · Cited by 322 · see citing works
Feasible generalized least squares for panel data with cross-sectional and serial correlations
Bai, J., Choi, S. H., & Liao, Y. (2020) · Empirical Economics · doi:10.1007/s00181-020-01977-2 · Cited by 359 · see citing works
“A widely used class of robust standard errors is clustered standard errors, for example, Petersen (2009), Wooldridge (2010) and Cameron and Miller (2015).”
BackgroundMethodAugmented Reality in Retail and Its Impact on Sales
Tan, Y.-C., Chandukala, S. R., & Reddy, S. K. (2021) · Journal of Marketing · doi:10.1177/0022242921995449 · Cited by 322 · see citing works
Ever Failed, Try Again, Succeed Better: Results from a Randomized Educational Intervention on Grit
Alan, Ş., Boneva, T., & Ertaç, S. (2019) · The Quarterly Journal of Economics · doi:10.1093/qje/qjz006 · Cited by 330 · see citing works
Randomization Inference with Stata: A Guide and Software
Heß, S. (2017) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x1701700306 · Cited by 320 · see citing works
Mapping the carbon footprint of EU regions
Ivanova, D., Vita, G., Steen‐Olsen, K., Stadler, K., Melo, P. C., Wood, R. A., & Hertwich, E. G. (2017) · Environmental Research Letters · doi:10.1088/1748-9326/aa6da9 · Cited by 316 · see citing works
The Effects of Teacher Match on Students’ Academic Perceptions and Attitudes
Egalite, A. J., & Kisida, B. (2017) · Educational Evaluation and Policy Analysis · doi:10.3102/0162373717714056 · Cited by 310 · see citing works
Sharing riders: How bikesharing impacts bus ridership in New York City
Campbell, K., & Brakewood, C. (2017) · Transportation Research Part A Policy and Practice · doi:10.1016/j.tra.2017.04.017 · Cited by 298 · see citing works
The wild bootstrap for few (treated) clusters
MacKinnon, J. G., & Webb, M. D. (2018) · The Econometrics Journal · doi:10.1111/ectj.12107 · Cited by 317 · see citing works
Sommers, B. D., Maylone, B., Blendon, R. J., Orav, E. J., & Epstein, A. M. (2017) · Health Affairs · doi:10.1377/hlthaff.2017.0293 · Cited by 286 · see citing works
Impact evaluation using Difference-in-Differences
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The Role of Family Support in Facilitating Academic Success of Low-Income Students
Roksa, J., & Kinsley, P. (2018) · Research in Higher Education · doi:10.1007/s11162-018-9517-z · Cited by 276 · see citing works
A community college instructor like me: Race and ethnicity interactions in the classroom
Fairlie, R. W., Hoffmann, F., & Oreopoulos, P. (2014) · American Economic Review · doi:10.1257/aer.104.8.2567 · Cited by 274 · see citing works
Do China's high-speed-rail projects promote local economy?—New evidence from a panel data approach
Ke, X., Chen, H., Hong, Y., & Hsiao, C. (2017) · China Economic Review · doi:10.1016/j.chieco.2017.02.008 · Cited by 272 · see citing works
Dividends and economic policy uncertainty: International evidence
Attig, N., Ghoul, S. E., Guedhami, O., & Zheng, X. (2020) · Journal of Corporate Finance · doi:10.1016/j.jcorpfin.2020.101785 · Cited by 270 · see citing works
The robust error meta-regression method for dose–response meta-analysis
Xu, C., & Doi, S. A. R. (2017) · International Journal of Evidence-Based Healthcare · doi:10.1097/xeb.0000000000000132 · Cited by 240 · see citing works
Do fiscal rules constrain fiscal policy? A meta-regression-analysis
Heinemann, F., Moessinger, M.-D., & Yeter, M. (2017) · European Journal of Political Economy · doi:10.1016/j.ejpoleco.2017.03.008 · Cited by 235 · see citing works
Earnings Smoothing: For Good or Evil?
Demerjian, P. R., Lewis‐Western, M. F., & McVay, S. E. (2014) · Journal of Accounting Auditing & Finance · doi:10.1177/0148558x17748405 · Cited by 247 · see citing works
Pan, Y., Siegel, S., & Wang, T. Y. (2017) · Journal of Financial and Quantitative Analysis · doi:10.1017/s0022109017000771 · Cited by 235 · see citing works
Carbon Emissions and the Bank-Lending Channel
Kacperczyk, M. T., & Peydró, J. (2026) · Review of Financial Studies · doi:10.1093/rfs/hhag078 · Cited by 232 · see citing works
The influence of business strategy on annual report readability
Lim, E. K., Chalmers, K., & Hanlon, D. (2018) · Journal of Accounting and Public Policy · doi:10.1016/j.jaccpubpol.2018.01.003 · Cited by 226 · see citing works
Fiction reading has a small positive impact on social cognition: A meta-analysis.
Dodell-Feder, D., & Tamir, D. I. (2018) · Journal of Experimental Psychology: General · doi:10.1037/xge0000395 · Cited by 223 · see citing works
Jensen, U. T., & Bro, L. L. (2017) · The American Review of Public Administration · doi:10.1177/0275074017699470 · Cited by 238 · see citing works
clubSandwich: Cluster-Robust (Sandwich) Variance Estimators with Small-Sample Corrections
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Home away from home? Foreign demand and London house prices
Badarinza, C., & Ramadorai, T. (2018) · Journal of Financial Economics · doi:10.1016/j.jfineco.2018.07.010 · Cited by 209 · see citing works
Teo, I., Chay, J., Cheung, Y. B., Sung, S. C., Tewani, K. G., Yeo, L., Yang, G. M., Pan, F. T., Ng, J. Y., Aloweni, F. B. A. B., et al. (2021) · PLoS ONE · doi:10.1371/journal.pone.0258866 · Cited by 229 · see citing works
“Analyses were conducted using Stata version 15�1 [21] and statistical inference was based on cluster-robust standard errors (SEs) at the individual level [22] and the 5% significance level.”
MethodAntonakis, J., Bastardoz, N., & Rönkkö, M. (2019) · Organizational Research Methods · doi:10.1177/1094428119877457 · Cited by 213 · see citing works
Cawley, J., Thow, A. M., Wen, K. J., & Frisvold, D. (2019) · Annual Review of Nutrition · doi:10.1146/annurev-nutr-082018-124603 · Cited by 207 · see citing works
Armed conflict and child mortality in Africa: a geospatial analysis
Wagner, Z., Heft-Neal, S., Bhutta, Z. A., Black, R. E., Burke, M., & Bendavid, E. (2018) · The Lancet · doi:10.1016/s0140-6736(18)31437-5 · Cited by 200 · see citing works
Organized Crime, Violence, and Politics
Alesina, A., Piccolo, S., & Pinotti, P. (2018) · The Review of Economic Studies · doi:10.1093/restud/rdy036 · Cited by 203 · see citing works
Population density and urban air quality
Borck, R., & Schrauth, P. (2020) · Regional Science and Urban Economics · doi:10.1016/j.regsciurbeco.2020.103596 · Cited by 203 · see citing works
Rural household energy consumption characteristics and determinants in China
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Cognitive fatigue influences students’ performance on standardized tests
Sievertsen, H. H., Gino, F., & Piovesan, M. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1516947113 · Cited by 194 · see citing works
The Effect of Corporate Taxation on Investment and Financial Policy: Evidence from the DPAD
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Heterogeneity and predictors of the effects of AI assistance on radiologists
Yu, F., Moehring, A., Banerjee, O., Salz, T., Agarwal, N., & Rajpurkar, P. (2024) · Nature Medicine · doi:10.1038/s41591-024-02850-w · Cited by 200 · see citing works
Musafiri, C. M., Kiboi, M., Macharia, J. M., Ng’etich, O. K., Kosgei, D. K., Mulianga, B. A., Okoti, M., & Ngetich, F. K. (2021) · Heliyon · doi:10.1016/j.heliyon.2021.e08677 · Cited by 193 · see citing works
“The ordered outcome could be assessed as a latent variable Y*, where Y* is the unobservable measure of smallholders' CSAPs adoption intensity [6, 35] as described in Eq.”
BackgroundNurse practitioner independence, health care utilization, and health outcomes
Traczynski, J., & Udalova, V. M. (2018) · Journal of Health Economics · doi:10.1016/j.jhealeco.2018.01.001 · Cited by 192 · see citing works
Corruption and Corporate Innovation
Ellis, J. A., Smith, J. D., & White, R. (2019) · Journal of Financial and Quantitative Analysis · doi:10.1017/s0022109019000735 · Cited by 194 · see citing works
Effects of an Intervention to Reduce Hospitalizations From Nursing Homes
Kane, R. L., Huckfeldt, P. J., Tappen, R. M., Engström, G., Rojido, C., Newman, D., Yang, Z., & Ouslander, J. G. (2017) · JAMA Internal Medicine · doi:10.1001/jamainternmed.2017.2657 · Cited by 190 · see citing works
Highway toll and air pollution: Evidence from Chinese cities
Fu, S., & Gu, Y. (2016) · Journal of Environmental Economics and Management · doi:10.1016/j.jeem.2016.11.007 · Cited by 190 · see citing works
Song, S., Lian, J., Skowronski, K., & Yan, T. (2023) · Journal of Operations Management · doi:10.1002/joom.1272 · Cited by 184 · see citing works
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Li, J., Liu, B., & Qian, G. (2019) · Journal of World Business · doi:10.1016/j.jwb.2019.04.004 · Cited by 187 · see citing works
The Economic Aftermath of Resource Booms: Evidence from Boomtowns in the American West
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Randomization inference for difference-in-differences with few treated clusters
MacKinnon, J. G., & Webb, M. D. (2020) · Journal of Econometrics · doi:10.1016/j.jeconom.2020.04.024 · Cited by 182 · see citing works
Do credit constraints favor dirty production? Theory and plant-level evidence
Andersen, D. C. (2017) · Journal of Environmental Economics and Management · doi:10.1016/j.jeem.2017.04.002 · Cited by 176 · see citing works
Doing Well by Making Well: The Impact of Corporate Wellness Programs on Employee Productivity
Gubler, T., Larkin, I., & Pierce, L. (2018) · Management Science · doi:10.1287/mnsc.2017.2883 · Cited by 222 · see citing works
Tobit models in strategy research: Critical issues and applications
Amore, M. D., & Murtinu, S. (2019) · Global Strategy Journal · doi:10.1002/gsj.1363 · Cited by 173 · see citing works
“As shown, for instance, by Cameron and Miller (2015), serial correlation within clusters likely leads to a large difference between unadjusted SEs and clustered ones.”
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Earnings Inequality and the Minimum Wage: Evidence from Brazil
Engbom, N., & Moser, C. (2022) · American Economic Review · doi:10.1257/aer.20181506 · Cited by 172 · see citing works
Climate change and corporate cash holdings: Global evidence
Javadi, S., Masum, A. A., Aram, M., & Rao, R. P. (2023) · Financial Management · doi:10.1111/fima.12420 · Cited by 170 · see citing works
The impact of Covid-19 on student achievement: Evidence from a recent meta-analysis
Di Pietro, G. (2023) · Educational Research Review · doi:10.1016/j.edurev.2023.100530 · Cited by 173 · see citing works
“G. Di Pietro clusters (i.e., 39), following Cameron and Miller (2015) we apply the correction for small of clusters by employing wild score bootstrapping (Kline & Santos, 2012).”
InfluentialLet Them Eat Lunch: The Impact of Universal Free Meals on Student Performance
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Air pollution as a cause of sleeplessness: Social media evidence from a panel of Chinese cities
Heyes, A., & Zhu, M. (2019) · Journal of Environmental Economics and Management · doi:10.1016/j.jeem.2019.07.002 · Cited by 170 · see citing works
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- Authors
- Colin Cameron, A., & Miller, D. L.
- ORCID
- Miller, Douglas L.
- Venue
- Journal of Human Resources
- Publisher
- University of Wisconsin Press
- Published
- 2015
- Volume
- 50
- Issue
- 2
- Pages
- 317-372
- ISSN
- 0022-166X (ISSN-L)
- 1548-8004
- OpenAlex
- W2118836230
- Cited by
- 5,037
- References
- 83
- Citations by year
- 2026: 992 · 2025: 497 · 2024: 370 · 2023: 385 · 2022: 445 · 2021: 436 · 2020: 425 · 2019: 358 · 2018: 396 · 2017: 344 · 2016: 225 · 2015: 115 · 2014: 32 · 2013: 8 · 2012: 4
- FWCI
- 321.44
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The Journal of Human Resources (publishedVersion)
- Project Muse (Johns Hopkins University) (submittedVersion)
- eScholarship (California Digital Library) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- cluster-robust standard errors, clustered data, intra-cluster correlation, regression inference, ordinary least squares, estimator precision
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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