We consider the problem of determining the optimal accuracy of public statistics when increased accuracy requires a loss of privacy. To formalize this allocation problem, we use tools from statistics and computer science to model the publication technology used by a public statistical agency. We derive the demand for accurate statistics from first principles to generate interdependent preferences that account for the public-good nature of both data accuracy and privacy loss. We first show data accuracy is inefficiently undersupplied by a private provider. Solving the appropriate social planner's problem produces an implementable publication strategy. We implement the socially optimal publication plan for statistics on income and health status using data from the American Community Survey, National Health Interview Survey, Federal Statistical System Public Opinion Survey and Cornell National Social Survey. Our analysis indicates that welfare losses from providing too much privacy protection and, therefore, too little accuracy can be substantial.
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An Economic Analysis of Privacy Protection and Statistical Accuracy as Social Choices
August 2018
Working Paper Number:
CES-18-35
Statistical agencies face a dual mandate to publish accurate statistics while protecting respondent privacy. Increasing privacy protection requires decreased accuracy. Recognizing this as a resource allocation problem, we propose an economic solution: operate where the marginal cost of increasing privacy equals the marginal benefit. Our model of production, from computer science, assumes data are published using an efficient differentially private algorithm. Optimal choice weighs the demand for accurate statistics against the demand for privacy. Examples from U.S. statistical programs show how our framework can guide decision-making. Further progress requires a better understanding of willingness-to-pay for privacy and statistical accuracy.
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Why the Economics Profession Must Actively Participate in the Privacy Protection Debate
March 2019
Working Paper Number:
CES-19-09
When Google or the U.S. Census Bureau publish detailed statistics on browsing habits or neighborhood characteristics, some privacy is lost for everybody while supplying public information. To date, economists have not focused on the privacy loss inherent in data publication. In their stead, these issues have been advanced almost exclusively by computer scientists who are primarily interested in technical problems associated with protecting privacy. Economists should join the discussion, first, to determine where to balance privacy protection against data quality; a social choice problem. Furthermore, economists must ensure new privacy models preserve the validity of public data for economic research.
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Releasing Earnings Distributions using Differential Privacy: Disclosure Avoidance System For Post Secondary Employment Outcomes (PSEO)
April 2019
Working Paper Number:
CES-19-13
The U.S. Census Bureau recently released data on earnings percentiles of graduates from post secondary institutions. This paper describes and evaluates the disclosure avoidance system developed for these statistics. We propose a differentially private algorithm for releasing these data based on standard differentially private building blocks, by constructing a histogram of earnings and the application of the Laplace mechanism to recover a differentially-private CDF of earnings. We demonstrate that our algorithm can release earnings distributions with low error, and our algorithm out-performs prior work based on the concept of smooth sensitivity from Nissim, Raskhodnikova and Smith (2007).
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An In-Depth Examination of Requirements for Disclosure Risk Assessment
October 2023
Authors:
Ron Jarmin,
John M. Abowd,
Ian M. Schmutte,
Jerome P. Reiter,
Nathan Goldschlag,
Victoria A. Velkoff,
Michael B. Hawes,
Robert Ashmead,
Ryan Cumings-Menon,
Sallie Ann Keller,
Daniel Kifer,
Philip Leclerc,
Rolando A. RodrÃguez,
Pavel Zhuravlev
Working Paper Number:
CES-23-49
The use of formal privacy to protect the confidentiality of responses in the 2020 Decennial Census of Population and Housing has triggered renewed interest and debate over how to measure the disclosure risks and societal benefits of the published data products. Following long-established precedent in economics and statistics, we argue that any proposal for quantifying disclosure risk should be based on pre-specified, objective criteria. Such criteria should be used to compare methodologies to identify those with the most desirable properties. We illustrate this approach, using simple desiderata, to evaluate the absolute disclosure risk framework, the counterfactual framework underlying differential privacy, and prior-to-posterior comparisons. We conclude that satisfying all the desiderata is impossible, but counterfactual comparisons satisfy the most while absolute disclosure risk satisfies the fewest. Furthermore, we explain that many of the criticisms levied against differential privacy would be levied against any technology that is not equivalent to direct, unrestricted access to confidential data. Thus, more research is needed, but in the near-term, the counterfactual approach appears best-suited for privacy-utility analysis.
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A Simulated Reconstruction and Reidentification Attack on the 2010 U.S. Census: Full Technical Report
December 2023
Authors:
Lars Vilhuber,
John M. Abowd,
Ethan Lewis,
Nathan Goldschlag,
Robert Ashmead,
Daniel Kifer,
Philip Leclerc,
Rolando A. RodrÃguez,
Tamara Adams,
David Darais,
Sourya Dey,
Simson L. Garfinkel,
Scott Moore,
Ramy N. Tadros
Working Paper Number:
CES-23-63R
For the last half-century, it has been a common and accepted practice for statistical agencies, including the United States Census Bureau, to adopt different strategies to protect the confidentiality of aggregate tabular data products from those used to protect the individual records contained in publicly released microdata products. This strategy was premised on the assumption that the aggregation used to generate tabular data products made the resulting statistics inherently less disclosive than the microdata from which they were tabulated. Consistent with this common assumption, the 2010 Census of Population and Housing in the U.S. used different disclosure limitation rules for its tabular and microdata publications. This paper demonstrates that, in the context of disclosure limitation for the 2010 Census, the assumption that tabular data are inherently less disclosive than their underlying microdata is fundamentally flawed. The 2010 Census published more than 150 billion aggregate statistics in 180 table sets. Most of these tables were published at the most detailed geographic level'individual census blocks, which can have populations as small as one person. Using only 34 of the published table sets, we reconstructed microdata records including five variables (census block, sex, age, race, and ethnicity) from the confidential 2010 Census person records. Using only published data, an attacker using our methods can verify that all records in 70% of all census blocks (97 million people) are perfectly reconstructed. We further confirm, through reidentification studies, that an attacker can, within census blocks with perfect reconstruction accuracy, correctly infer the actual census response on race and ethnicity for 3.4 million vulnerable population uniques (persons with race and ethnicity different from the modal person on the census block) with 95% accuracy. Having shown the vulnerabilities inherent to the disclosure limitation methods used for the 2010 Census, we proceed to demonstrate that the more robust disclosure limitation framework used for the 2020 Census publications defends against attacks that are based on reconstruction. Finally, we show that available alternatives to the 2020 Census Disclosure Avoidance System would either fail to protect confidentiality, or would overly degrade the statistics' utility for the primary statutory use case: redrawing the boundaries of all of the nation's legislative and voting districts in compliance with the 1965 Voting Rights Act. You are reading the full technical report. For the summary paper see https://doi.org/10.1162/99608f92.4a1ebf70.
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Simultaneous Edit-Imputation for Continuous Microdata
December 2015
Working Paper Number:
CES-15-44
Many statistical organizations collect data that are expected to satisfy linear constraints; as examples, component variables should sum to total variables, and ratios of pairs of variables should be bounded by expert-specified constants. When reported data violate constraints, organizations identify and replace values potentially in error in a process known as edit-imputation. To date, most approaches separate the error localization and imputation steps, typically using optimization methods to identify the variables to change followed by hot deck imputation. We present an approach that fully integrates editing and imputation for continuous microdata under linear constraints. Our approach relies on a Bayesian hierarchical model that includes (i) a flexible joint probability model for the underlying true values of the data with support only on the set of values that satisfy all editing constraints, (ii) a model for latent indicators of the variables that are in error, and (iii) a model for the reported responses for variables in error. We illustrate the potential advantages of the Bayesian editing approach over existing approaches using simulation studies. We apply the model to edit faulty data from the 2007 U.S. Census of Manufactures. Supplementary materials for this article are available online.
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A Simulated Reconstruction and Reidentification Attack on the 2010 U.S. Census
August 2025
Authors:
Lars Vilhuber,
John M. Abowd,
Ethan Lewis,
Nathan Goldschlag,
Michael B. Hawes,
Robert Ashmead,
Daniel Kifer,
Philip Leclerc,
Rolando A. RodrÃguez,
Tamara Adams,
David Darais,
Sourya Dey,
Simson L. Garfinkel,
Scott Moore,
Ramy N. Tadros
Working Paper Number:
CES-25-57
For the last half-century, it has been a common and accepted practice for statistical agencies, including the United States Census Bureau, to adopt different strategies to protect the confidentiality of aggregate tabular data products from those used to protect the individual records contained in publicly released microdata products. This strategy was premised on the assumption that the aggregation used to generate tabular data products made the resulting statistics inherently less disclosive than the microdata from which they were tabulated. Consistent with this common assumption, the 2010 Census of Population and Housing in the U.S. used different disclosure limitation rules for its tabular and microdata publications. This paper demonstrates that, in the context of disclosure limitation for the 2010 Census, the assumption that tabular data are inherently less disclosive than their underlying microdata is fundamentally flawed. The 2010 Census published more than 150 billion aggregate statistics in 180 table sets. Most of these tables were published at the most detailed geographic level'individual census blocks, which can have populations as small as one person. Using only 34 of the published table sets, we reconstructed microdata records including five variables (census block, sex, age, race, and ethnicity) from the confidential 2010 Census person records. Using only published data, an attacker using our methods can verify that all records in 70% of all census blocks (97 million people) are perfectly reconstructed. We further confirm, through reidentification studies, that an attacker can, within census blocks with perfect reconstruction accuracy, correctly infer the actual census response on race and ethnicity for 3.4 million vulnerable population uniques (persons with race and ethnicity different from the modal person on the census block) with 95% accuracy. Having shown the vulnerabilities inherent to the disclosure limitation methods used for the 2010 Census, we proceed to demonstrate that the more robust disclosure limitation framework used for the 2020 Census publications defends against attacks that are based on reconstruction. Finally, we show that available alternatives to the 2020 Census Disclosure Avoidance System would either fail to protect confidentiality, or would overly degrade the statistics' utility for the primary statutory use case: redrawing the boundaries of all of the nation's legislative and voting districts in compliance with the 1965 Voting Rights Act.
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Interactions, Neighborhood Selection, and Housing Demand
August 2002
Working Paper Number:
CES-02-19
This paper contributes to the growing literature that identifies and measures the impact of social context on individual economic behavior. We develop a model of housing demand with neighborhood e'ects and neighborhood choice. Modelling neighborhood choice is of fundamental importance in estimating and understanding endogenous and exogenous neighborhood effects. That is, to obtain unbiased estimates of neighborhood effects, it is necessary to control for non-random sorting into neighborhoods. Estimation of the model exploits a unique data set of household data that has been augmented with contextual information at two di'erent levels ('scales') of aggregation. One is at the neighborhood cluster level, of about ten neighbors, with the data coming from a special sample of the American Housing Survey. A second level is the census tract to which these dwelling units belong. Tract-level data are available in the Summary Tape Files of the decennial Census data. We merge these two data sets by gaining access to confidential data of the U.S. Bureau of the Census. We overcome some limitations of these data by implementing some significant methodological advances in estimating discrete choice models. Our results for the neighborhood choice model indicate that individuals prefer to live near others like themselves. This can perpetuate income inequality since those with the best opportunities at economic success will cluster together. The results for the housing demand equation are similar to those in our earlier work [Ioannides and Zabel (2000] where we find evidence of significant endogenous and contextual neighborhood effects.
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MISCLASSIFICATION IN BINARY CHOICE MODELS
May 2013
Working Paper Number:
CES-13-27
We derive the asymptotic bias from misclassification of the dependent variable in binary choice models. Measurement error is necessarily non-classical in this case, which leads to bias in linear and non-linear models even if only the dependent variable is mismeasured. A Monte Carlo study and an application to food stamp receipt show that the bias formulas are useful to analyze the sensitivity of substantive conclusions, to interpret biased coefficients and imply features of the estimates that are robust to misclassification. Using administrative records linked to survey data as validation data, we examine estimators that are consistent under misclassification. They can improve estimates if their assumptions hold, but can aggravate the problem if the assumptions are invalid. The estimators differ
in their robustness to such violations, which can be improved by incorporating additional information. We propose tests for the presence and nature of misclassification that can help to choose an estimator.
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Distribution Preserving Statistical Disclosure Limitation
September 2006
Working Paper Number:
tp-2006-04
One approach to limiting disclosure risk in public-use microdata is to release multiply-imputed,
partially synthetic data sets. These are data on actual respondents, but with confidential data
replaced by multiply-imputed synthetic values. A mis-specified imputation model can invalidate
inferences because the distribution of synthetic data is completely determined by the model used
to generate them. We present two practical methods of generating synthetic values when the imputer
has only limited information about the true data generating process. One is applicable when
the true likelihood is known up to a monotone transformation. The second requires only limited
knowledge of the true likelihood, but nevertheless preserves the conditional distribution of the confidential
data, up to sampling error, on arbitrary subdomains. Our method maximizes data utility
and minimizes incremental disclosure risk up to posterior uncertainty in the imputation model and
sampling error in the estimated transformation. We validate the approach with a simulation and
application to a large linked employer-employee database.
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