Conditions for swappability of records in a microdata set when some marginals are fixed

We consider swapping of two records in a microdata set for the purpose of disclosure control. We give some necessary and sufficient conditions that some observations can be swapped between two records under the restriction that a given set of marginals are fixed. We also give an algorithm to find another record for swapping if one wants to swap out some observations from a particular record.     

Bayesian Estimation of Discrete Multivariate Latent Structure Models With Structural Zeros

In multivariate categorical data, models based on conditional independence assumptions, such as latent class models, offer efficient estimation of complex dependencies. However, Bayesian versions of latent structure models for categorical data typically do not appropriately handle impossible combinations of variables, also known as structural zeros. Allowing nonzero probability for impossible combinations results in inaccurate estimates of joint and conditional probabilities, even for feasible combinations. We present an approach for estimating posterior distributions in Bayesian latent structure models with potentially many structural zeros. The basic idea is to treat the observed data as a truncated sample from an augmented dataset, thereby allowing us to exploit the conditional independence assumptions for computational expediency. As part of the approach, we develop an algorithm for collapsing a large set of structural zero combinations into a much smaller set of disjoint marginal conditions, which speeds up computation. We apply the approach to sample from a semiparametric version of the latent class model with structural zeros in the context of a key issue faced by national statistical agencies seeking to disseminate confidential data to the public: estimating the number of records in a sample that are unique in the population on a set of publicly available categorical variables. The latent class model offers remarkably accurate estimates of population uniqueness, even in the presence of a large number of structural zeros.     

Using Global Optimization to Estimate Population Class Sizes

In this paper we formulate a nonlinear optimization model to estimate population class sizes based on sample information. The model is nonconvex and has several local minima corresponding to different populations that could have been the source of the sample data. We show that many if not all local solutions can be found using a new global optimization algorithm called OptQuest/NLP (OQNLP). This can be used to estimate the number of individuals in a population with unique or rarely occurring characteristics, which is useful for assessing disclosure risk. It can also be used to estimate the number of classes in a population, a problem with applications in a variety of disciplines.     

Public Disclosure Programs vs. traditional approaches for environmental regulation: Green goodwill and the policies of the firm

A Public Disclosure Program (PDP) is compared to a traditional environmental regulation (exemplified by a tax/subsidy) in a simple dynamic framework. A PDP aims at revealing the environmental record of firms to the public. This information affects its image (goodwill or brand equity), and ultimately its profit. A firm polluting less than its prescribed target would win consumer’s sympathy and raise its goodwill, whereas it is the other way around when the firm exceeds its emissions quota. The evolution of this goodwill is assumed to depend also on green activities or advertising expenditures. Within this framework, we analyze how a PDP affects the firm’s optimal policies regarding emissions, pricing and advertising as compared to a traditional regulation. We show that advertising acts as a complementary device to pricing and that emissions are increasing in goodwill. The role of a standard or target level for emissions turns out to be totally different under both policy regimes. In the case of a tax/subsidy approach, this target level only acts as constant who increases or decreases profit by a fixed amount, but it does not affect the policy of the firm. On the contrary, if a PDP is implemented, the target value for emissions enters in an important way in the goodwill accumulation mechanism and determines how the firm reacts to the regulation and what is the time path for the economic and environmental variables. Moreover, this value is also crucial to determine the possibility that a PDP is profit improving. A policy implication of this fact is that regulators should be particularly careful in fixing the emission standard when a PDP is applied. The theoretical results are complemented with a numerical illustration.     

Differentially Private Significance Tests for Regression Coefficients

Many data producers seek to provide users access to confidential data without unduly compromising data subjects’ privacy and confidentiality. One general strategy is to require users to do analyses without seeing the confidential data; for example, analysts only get access to synthetic data or query systems that provide disclosure-protected outputs of statistical models. With synthetic data or redacted outputs, the analyst never really knows how much to trust the resulting findings. In particular, if the user did the same analysis on the confidential data, would regression coefficients of interest be statistically significant or not? We present algorithms for assessing this question that satisfy differential privacy. We describe conditions under which the algorithms should give accurate answers about statistical significance. We illustrate the properties of the proposed methods using artificial and genuine data. Supplementary materials for this article are available online.