In causal mediation analysis, nonparametric identification of the natural indirect effect typically relies on, in addition to no unobserved pre-exposure confounding, fundamental assumptions of (i) so-called \"cross-world-countterfactuals\" independence and (ii) no exposure-induced confounding. When the mediator is binary, bounds for partial identification have been given when neither assumption is made, or alternatively when assuming only (ii). We extend existing bounds to the case of a polytomous mediator, and provide bounds for the case assuming only (i). We apply these bounds to data from the Harvard PEPFAR program in Nigeria, where we evaluate the extent to which the effects of antiretroviral therapy on virological failure are mediated by a patient\'s adherence, and show that inference on this effect is somewhat sensitive to model assumptions.

We use data from the National Longitudinal Study of Adolescent to Adult Health to investigate whether the quality of tertiary education -measured by college selectivity-causally affects obesity prevalence in the medium run (by age 24-34) and in the longer run (about 10 years later). We use partial identification methods, which allow us, while relying on weak assumptions, to overcome the potential endogeneity of college selectivity as well as the potential violation of the stable unit treatment value assumption due to students interacting with each other, and to obtain informative identification regions for the average treatment effect of college selectivity on obesity. We find that attending a more selective college causally reduces obesity, both in the medium and in the longer run. We provide evidence that the mechanisms through which the impact of college selectivity on obesity operates include an increase in income, a reduction in physical inactivity and in the consumption of fast food and sweetened drinks.

HIV estimation using data from the demographic and health surveys (DHS) is limited by the presence of non-response and test refusals. Conventional adjustments such as imputation require the data to be missing at random. Methods that use instrumental variables allow the possibility that prevalence is different between the respondents and non-respondents, but their performance depends critically on the validity of the instrument. Using Manski\'s partial identification approach, we form instrumental variable bounds for HIV prevalence from a pool of candidate instruments. Our method does not require all candidate instruments to be valid. We use a simulation study to evaluate and compare our method against its competitors. We illustrate the proposed method using DHS data from Zambia, Malawi and Kenya. Our simulations show that imputation leads to seriously biased results even under mild violations of non-random missingness. Using worst case identification bounds that do not make assumptions about the non-response mechanism is robust but not informative. By taking the union of instrumental variable bounds balances informativeness of the bounds and robustness to inclusion of some invalid instruments. Non-response and refusals are ubiquitous in population based HIV data such as those collected under the DHS. Partial identification bounds provide a robust solution to HIV prevalence estimation without strong assumptions. Union bounds are significantly more informative than the worst case bounds without sacrificing credibility.

Capture-recapture (CRC) surveys are used to estimate the size of a population whose members cannot be enumerated directly. CRC surveys have been used to estimate the number of Coronavirus Disease 2019 (COVID-19) infections, people who use drugs, sex workers, conflict casualties, and trafficking victims. When k-capture samples are obtained, counts of unit captures in subsets of samples are represented naturally by a 2k contingency table in which one element-the number of individuals appearing in none of the samples-remains unobserved. In the absence of additional assumptions, the population size is not identifiable (i.e., point identified). Stringent assumptions about the dependence between samples are often used to achieve point identification. However, real-world CRC surveys often use convenience samples in which the assumed dependence cannot be guaranteed, and population size estimates under these assumptions may lack empirical credibility. In this work, we apply the theory of partial identification to show that weak assumptions or qualitative knowledge about the nature of dependence between samples can be used to characterize a nontrivial confidence set for the true population size. We construct confidence sets under bounds on pairwise capture probabilities using two methods: test inversion bootstrap confidence intervals and profile likelihood confidence intervals. Simulation results demonstrate well-calibrated confidence sets for each method. In an extensive real-world study, we apply the new methodology to the problem of using heterogeneous survey data to estimate the number of people who inject drugs in Brussels, Belgium.

Although mental health conditions are known to be associated with socioeconomic hardships, their causal effects remain largely unexplored. Using a sample of low-income families in the National Health Interview Survey (NHIS), we assess causal effects of serious mental illness (SMI) and related mental health conditions on family food security. We apply partial identification methods to account for fundamental endogeneity and measurement identification problems in a unified framework. To implement these methods, we combine a proxy measure of SMI in the NHIS with an estimate of the true rate of SMI from the Substance Abuse and Mental Health Services Administration. We also develop an innovative approach to approximate true prevalence rates when only self-reported prevalence rates are available. Applying relatively weak monotonicity assumptions on latent food security outcomes, we find that alleviating SMI would improve the food security rate by at least 9.5 percentage points, or 15 %. JEL codes: C21, I10, I38.

Expanded access to health care often leads to new diagnoses for previously undetected conditions. New diagnoses make it difficult to identify the causal effect of expanding health insurance on individuals with particular diagnoses: the newly diagnosed in the treatment group are likely to differ in unobserved ways from the control group. This paper provides two methods for dealing with this problem depending on the data available to the researcher and diagnosis-specific knowledge. If there is no panel dimension to the data, then the causal effect for the subgroup of interest can be bounded from either above or below depending on the condition in question. If panel data are available, then the newly diagnosed can be identified, and their treated outcomes subtracted from the overall effect of interest. I apply these methods to find that the difference-in-discontinuities estimator underestimates the effect of Medicare prescription drug coverage on the uptake of insulin by first-time users by 20%.

Many partial identification problems can be characterized by the optimal value of a function over a set where both the function and set need to be estimated by empirical data. Despite some progress for convex problems, statistical inference in this general setting remains to be developed. To address this, we derive an asymptotically valid confidence interval for the optimal value through an appropriate relaxation of the estimated set. We then apply this general result to the problem of selection bias in population-based cohort studies. We show that existing sensitivity analyses, which are often conservative and difficult to implement, can be formulated in our framework and made significantly more informative via auxiliary information on the population. We conduct a simulation study to evaluate the finite sample performance of our inference procedure, and conclude with a substantive motivating example on the causal effect of education on income in the highly selected UK Biobank cohort. We demonstrate that our method can produce informative bounds using plausible population-level auxiliary constraints. We implement this method in the [Formula: see text] package [Formula: see text].

The polychoric correlation is a popular measure of association for ordinal data. It estimates a latent correlation, i.e., the correlation of a latent vector. This vector is assumed to be bivariate normal, an assumption that cannot always be justified. When bivariate normality does not hold, the polychoric correlation will not necessarily approximate the true latent correlation, even when the observed variables have many categories. We calculate the sets of possible values of the latent correlation when latent bivariate normality is not necessarily true, but at least the latent marginals are known. The resulting sets are called partial identification sets, and are shown to shrink to the true latent correlation as the number of categories increase. Moreover, we investigate partial identification under the additional assumption that the latent copula is symmetric, and calculate the partial identification set when one variable is ordinal and another is continuous. We show that little can be said about latent correlations, unless we have impractically many categories or we know a great deal about the distribution of the latent vector. An open-source R package is available for applying our results.

This paper provides a general framework for analyzing self-confirming policies. We study self-confirming equilibria in recurrent decision problems with incomplete information about the true stochastic model. We characterize stationary monetary policies in a linear-quadratic setting.

As a fundamental component of health care, disease screening is of highly importance. Oftentimes, two screening tests for a specific disease are compared in order to determine an optimal screening policy, for example, the digital rectal examination (DRE) and serum prostate specific antigen (PSA) level for screening prostate cancer. Ideally, if a gold standard test is given to each individual being screened to establish their true disease status, the difference in accuracy measures between two tests can be evaluated. In practice, however, it is common that only individuals who test positive on at least one screening test are to receive gold standard tests, which are often invasive and cannot be applied to those with negative results on both tests due to ethical reasons. Under such circumstances, estimates of the differences in accuracy measures between two tests cannot be determined, thus the inference problem within this framework is challenging. In this article, using sensitivity and specificity as measures of test accuracy, we show that their difference between two tests is interval-identified, as bounded by estimable sharp bounds. Here, we develop the asymptotic normality for the estimators of the bounds and construct confidence intervals for the difference by utilizing the method for solving inference problem for partially identified parameters. The performance of constructed confidence intervals for the difference and their sharp bounds are evaluated via simulation studies. We also apply the proposed method to the prostate cancer example to compare the accuracy of DRE and PSA.