Why Reduced-Form Regression Models of Health Effects Versus Exposures Should Not Replace QRA: Livestock Production and Infant Mortality as an Example

Do pollution emissions from livestock operations increase infant mortality rate (IMR)? A recent regression analysis of changes in IMR against changes in aggregate “animal units” (a weighted sum of cattle, pig, and poultry numbers) over time, for counties throughout the United States, suggested the provocative conclusion that they do: “[A] doubling of production leads to a 7.4% increase in infant mortality.” Yet, we find that regressing IMR changes against changes in specific components of “animal units” (cattle, pigs, and broilers) at the state level reveals statistically significant negative associations between changes in livestock production (especially, cattle production) and changes in IMR. We conclude that statistical associations between livestock variables and IMR variables are very sensitive to modeling choices (e.g., selection of explanatory variables, and use of specific animal types vs. aggregate “animal units). Such associations, whether positive or negative, do not warrant causal interpretation. We suggest that standard methods of quantitative risk assessment (QRA), including emissions release (source) models, fate and transport modeling, exposure assessment, and dose-response modeling, really are important—and indeed, perhaps, essential—for drawing valid causal inferences about health effects of exposures to guide sound, well-informed public health risk management policy. Reduced-form regression models, which skip most or all of these steps, can only quantify statistical associations (which may be due to model specification, variable selection, residual confounding, or other noncausal factors). Sound risk management requires the extra work needed to identify and model valid causal relations.     

Program Evaluation and Causal Inference With High‐Dimensional Data

In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data‐rich environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment effects, and function‐valued outcomes. Our framework covers the special case of exogenous receipt of treatment, either conditional on controls or unconditionally as in randomized control trials. In the latter case, our approach produces efficient estimators and honest bands for (functional) average treatment effects (ATE) and quantile treatment effects (QTE). To make informative inference possible, we assume that key reduced‐form predictive relationships are approximately sparse. This assumption allows the use of regularization and selection methods to estimate those relations, and we provide methods for post‐regularization and post‐selection inference that are uniformly valid (honest) across a wide range of models. We show that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reduced‐form functional parameters. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility and participation on accumulated assets. The results on program evaluation are obtained as a consequence of more general results on honest inference in a general moment‐condition framework, which arises from structural equation models in econometrics. Here, too, the crucial ingredient is the use of orthogonal moment conditions, which can be constructed from the initial moment conditions. We provide results on honest inference for (function‐valued) parameters within this general framework where any high‐quality, machine learning methods (e.g., boosted trees, deep neural networks, random forest, and their aggregated and hybrid versions) can be used to learn the nonparametric/high‐dimensional components of the model. These include a number of supporting auxiliary results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) offer a uniformly valid functional delta method, and (3) provide results for sparsity‐based estimation of regression functions for function‐valued outcomes.     

Comment on “Why Reduced‐Form Regression Models of Health Effects Versus Exposures Should Not Replace QRA: Livestock Production and Infant Mortality as an Example,” by Louis Anthony (Tony) Cox,Jr., Risk Analysis 2009, Vol. 29, No. 12

While a recent paper by Cox in this journal uses as its motivating factor the benefits of quantitative risk assessment, its content is entirely devoted to critiquing Sneeringer's article in the American Journal of Agricultural Economics. Cox's two main critiques of Sneeringer are fundamentally flawed and misrepresent the original article. Cox posits that Sneeringer did A and B, and then argues why A and B are incorrect. However, Sneeringer in fact did C and D; thus critiques of A and B are not applicable to Sneeringer's analysis.     

Heuristics Structure and Pervade Formal Risk Assessment

Lay perceptions of risk appear rooted more in heuristics than in reason. A major concern of the risk regulation literature is that such “error‐strewn” perceptions may be replicated in policy, as governments respond to the (mis)fears of the citizenry. This has led many to advocate a relatively technocratic approach to regulating risk, characterized by high reliance on formal risk and cost‐benefit analysis. However, through two studies of chemicals regulation, we show that the formal assessment of risk is pervaded by its own set of heuristics. These include rules to categorize potential threats, define what constitutes valid data, guide causal inference, and to select and apply formal models. Some of these heuristics lay claim to theoretical or empirical justifications, others are more back‐of‐the‐envelope calculations, while still more purport not to reflect some truth but simply to constrain discretion or perform a desk‐clearing function. These heuristics can be understood as a way of authenticating or formalizing risk assessment as a scientific practice, representing a series of rules for bounding problems, collecting data, and interpreting evidence (a methodology). Heuristics are indispensable elements of induction. And so they are not problematic per se, but they can become so when treated as laws rather than as contingent and provisional rules. Pitfalls include the potential for systematic error, masking uncertainties, strategic manipulation, and entrenchment. Our central claim is that by studying the rules of risk assessment qua rules, we develop a novel representation of the methods, conventions, and biases of the prior art.     

Confidence Intervals for Diffusion Index Forecasts and Inference for Factor‐Augmented Regressions

We consider the situation when there is a large number of series, N, each with T observations, and each series has some predictive ability for some variable of interest. A methodology of growing interest is first to estimate common factors from the panel of data by the method of principal components and then to augment an otherwise standard regression with the estimated factors. In this paper, we show that the least squares estimates obtained from these factor‐augmented regressions are consistent and asymptotically normal if . The conditional mean predicted by the estimated factors is consistent and asymptotically normal. Except when T/N goes to zero, inference should take into account the effect of “estimated regressors” on the estimated conditional mean. We present analytical formulas for prediction intervals that are valid regardless of the magnitude of N/T and that can also be used when the factors are nonstationary.     

Miscommunicating Risk,Uncertainty, and Causation: Fine Particulate Air Pollution and Mortality Risk as an Example

A recent paper in this journal (Fann et al., 2012) estimated that “about 80,000 premature mortalities would be avoided by lowering PM_2.5 levels to 5 μg/m³ nationwide” and that 2005 levels of PM_2.5 cause about 130,000 premature mortalities per year among people over age 29, with a 95% confidence interval of 51,000 to 200,000 premature mortalities per year.⁽¹⁾ These conclusions depend entirely on misinterpreting statistical coefficients describing the association between PM_2.5 and mortality rates in selected studies and models as if they were known to be valid causal coefficients. But they are not, and both the expert opinions of EPA researchers and analysis of data suggest that a true value of zero for the PM_2.5 mortality causal coefficient is not excluded by available data. Presenting continuous confidence intervals that exclude the discrete possibility of zero misrepresents what is currently known (and not known) about the hypothesized causal relation between changes in PM_2.5 levels and changes in mortality rates, suggesting greater certainty about projected health benefits than is justified.     

Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis

This paper considers nonstandard hypothesis testing problems that involve a nuisance parameter. We establish an upper bound on the weighted average power of all valid tests, and develop a numerical algorithm that determines a feasible test with power close to the bound. The approach is illustrated in six applications: inference about a linear regression coefficient when the sign of a control coefficient is known; small sample inference about the difference in means from two independent Gaussian samples from populations with potentially different variances; inference about the break date in structural break models with moderate break magnitude; predictability tests when the regressor is highly persistent; inference about an interval identified parameter; and inference about a linear regression coefficient when the necessity of a control is in doubt.     

Average and Quantile Effects in Nonseparable Panel Models

Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time‐homogeneity conditions that are like “time is randomly assigned” or “time is an instrument.” Partial‐identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects. It is shown that the usual, linear, fixed‐effects estimator is not a consistent estimator of the identified average effect, and a consistent estimator is given. A simple estimator of identified quantile treatment effects is given, providing a solution to the important problem of estimating quantile treatment effects from panel data. Bounds for overall effects in static and dynamic models are given. The dynamic bounds provide a partial‐identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity. The impact of T, the number of time periods, is shown by deriving shrinkage rates for the identified set as T grows. We also consider semiparametric, discrete‐choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds. Computationally convenient methods for semiparametric models are presented. We propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples. We give empirical illustrations.     

Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain

We develop results for the use of Lasso and post‐Lasso methods to form first‐stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post‐Lasso in the first stage is root‐n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well‐approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic “beta‐min” conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso‐based IV estimator with a data‐driven penalty performs well compared to recently advocated many‐instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso‐based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post‐Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non‐Gaussian, heteroscedastic disturbances that uses a data‐weighted ℓ₁‐penalty function. By innovatively using moderate deviation theory for self‐normalized sums, we provide convergence rates for the resulting Lasso and post‐Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that logp = o(n^1/3). We also provide a data‐driven method for choosing the penalty level that must be specified in obtaining Lasso and post‐Lasso estimates and establish its asymptotic validity under non‐Gaussian, heteroscedastic disturbances.     

Why Frequency is Not Well Defined for Engineering Systems with Nonexponential Failure Times

Dr. Yellman proposes to define frequency as “a time‐rate of events of a specified type over a particular time interval.” We review why no definition of frequency, including this one, can satisfy both of two conditions: (1) the definition should agree with the ordinary meaning of frequency, such as that less frequent events are less likely to occur than more frequent events, over any particular time interval for which the frequencies of both are defined; and (2) the definition should be applicable not only to exponentially distributed times between (or until) events, but also to some nonexponential (e.g., uniformly distributed) times. We make the simple point that no definition can satisfy (1) and (2) by showing that any definition that determines which of any two uniformly distributed times has the higher “frequency” (or that determines that they have the same “frequency,” if neither is higher) must assign a higher frequency number to the distribution with the lower probability of occurrence over some time intervals. Dr. Yellman's proposed phrase, “time‐rate of events … over a particular time interval” is profoundly ambiguous in such cases, as the instantaneous failure rates vary over an infinitely wide range (e.g., from one to infinity), making it unclear which value is denoted by the phrase “time‐rate of events.”     

Ice‐Breaker vs. Standalone: Comparing Alternative Workflow Modes of Mid‐level Care Providers

Capitalizing on the operational concept of division‐of‐labor, clinics often reduce physician service time by off‐loading some of his/her clinical activities to lower‐cost personnel. These personnel, such as nurse practitioners and physician assistants, are often collectively referred to as “mid‐level providers” (MLPs) and can perform many patient‐consultation tasks. The common rationale is that using an MLP allows the physician to serve more patients, increase patients’ access to care, and, due to MLPs’ lower salaries, improve the clinic's financial performance. An MLP is typically integrated into the outpatient clinic process in one of two modes: as an “ice‐breaker,” seeing each patient before the physician, or as a “standalone” provider, a substitute for the physician for the entirety of some patients’ visits. Despite both of these modes being widely used in practice, we find no research that identifies the circumstances under which either one is preferable. This study examines these two modes’ effects on operational performance, such as patient flow and throughput, as well as on financial measures. Using queueing and bottleneck analysis, discrete‐event simulation, and profit modeling, we compare these two deployment modes and identify the optimal policies for deploying MLPs as either ice‐breakers or as standalone providers. Interestingly, we also find there exists a range of scenarios where not hiring an MLP at all (i.e., the physician works alone) is likely to be most profitable for the clinic. Implications for practice are discussed.     

Construction of a Dose–Illness Relationship via Modeling Morbidity and Application to Risk Assessment of Wastewater Reuse

A disease burden (DB) evaluation for environmental pathogens is generally performed using disability‐adjusted life years with the aim of providing a quantitative assessment of the health hazard caused by pathogens. A critical step in the preparation for this evaluation is the estimation of morbidity between exposure and disease occurrence. In this study, the method of a traditional dose–response analysis was first reviewed, and then a combination of the theoretical basis of a “single‐hit” and an “infection‐illness” model was performed by incorporating two critical factors: the “infective coefficient” and “infection duration.” This allowed a dose–morbidity model to be built for direct use in DB calculations. In addition, human experimental data for typical intestinal pathogens were obtained for model validation, and the results indicated that the model was well fitted and could be further used for morbidity estimation. On this basis, a real case of a water reuse project was selected for model application, and the morbidity as well as the DB caused by intestinal pathogens during water reuse was evaluated. The results show that the DB attributed to Enteroviruses was significant, while that for enteric bacteria was negligible. Therefore, water treatment technology should be further improved to reduce the exposure risk of Enteroviruses . Since road flushing was identified as the major exposure route, human contact with reclaimed water through this pathway should be limited. The methodology proposed for model construction not only makes up for missing data of morbidity during risk evaluation, but is also necessary to quantify the maximum possible DB.     

Testing the babble hypothesis: Speaking time predicts leader emergence in small groups

The large, positive correlation between speaking time and leader emergence is well-established. As such, some authors have argued for a “babble hypothesis” of leadership, suggesting that only the quantity of speaking, not its quality, determines leader emergence. However, previous tests of this notion may have been problematic. Some studies have asserted a causal effect of speaking time on leader emergence based on experimental studies, but have limited participant communication, access to reliable information, or both. Other studies have used more ecologically valid designs, but have not always controlled for relevant participant traits or roles, suggesting potential endogeneity effects. Testing the babble hypothesis thus requires a study that is both ecologically valid and supports strong inference. The current study fills that gap and finds that speaking time retains its direct effect on leader emergence when accounting for intelligence, personality, gender, and the endogeneity of speaking time.     

Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models

This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. These models are often ill‐posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root‐n estimable or not. We provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is root‐n estimable or not. We establish the following new useful results: (1) the asymptotic normality of a plug‐in penalized sieve minimum distance (PSMD) estimator of a (possibly nonlinear) functional; (2) the consistency of simple sieve variance estimators for the plug‐in PSMD estimator, and hence the asymptotic chi‐square distribution of the sieve Wald statistic; (3) the asymptotic chi‐square distribution of an optimally weighted sieve quasi likelihood ratio (QLR) test under the null hypothesis; (4) the asymptotic tight distribution of a non‐optimally weighted sieve QLR statistic under the null; (5) the consistency of generalized residual bootstrap sieve Wald and QLR tests; (6) local power properties of sieve Wald and QLR tests and of their bootstrap versions; (7) asymptotic properties of sieve Wald and SQLR for functionals of increasing dimension. Simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.     

Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs

In the regression‐discontinuity (RD) design, units are assigned to treatment based on whether their value of an observed covariate exceeds a known cutoff. In this design, local polynomial estimators are now routinely employed to construct confidence intervals for treatment effects. The performance of these confidence intervals in applications, however, may be seriously hampered by their sensitivity to the specific bandwidth employed. Available bandwidth selectors typically yield a “large” bandwidth, leading to data‐driven confidence intervals that may be biased, with empirical coverage well below their nominal target. We propose new theory‐based, more robust confidence interval estimators for average treatment effects at the cutoff in sharp RD, sharp kink RD, fuzzy RD, and fuzzy kink RD designs. Our proposed confidence intervals are constructed using a bias‐corrected RD estimator together with a novel standard error estimator. For practical implementation, we discuss mean squared error optimal bandwidths, which are by construction not valid for conventional confidence intervals but are valid with our robust approach, and consistent standard error estimators based on our new variance formulas. In a special case of practical interest, our procedure amounts to running a quadratic instead of a linear local regression. More generally, our results give a formal justification to simple inference procedures based on increasing the order of the local polynomial estimator employed. We find in a simulation study that our confidence intervals exhibit close‐to‐correct empirical coverage and good empirical interval length on average, remarkably improving upon the alternatives available in the literature. All results are readily available in R and STATA using our companion software packages described in Calonico, Cattaneo, and Titiunik (2014d, 2014b).     

Instrumental Variable Estimation of Nonlinear Errors‐in‐Variables Models

This paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of Fourier transforms of conditional expectations of observable variables. For parametrically specified regression functions, we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged‐in nonparametric kernel density estimate. Both the identification and the estimation methodologies rely on Fourier analysis and on the theory of generalized functions. The finite‐sample properties of the estimator are investigated through Monte Carlo simulations.     

Lower Risk Bounds and Properties of Confidence Sets for Ill‐Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation,Unit Roots,and Estimation of Long Memory Parameters

Important estimation problems in econometrics like estimating the value of a spectral density at frequency zero, which appears in the econometrics literature in the guises of heteroskedasticity and autocorrelation consistent variance estimation and long run variance estimation, are shown to be “ill‐posed” estimation problems. A prototypical result obtained in the paper is that the minimax risk for estimating the value of the spectral density at frequency zero is infinite regardless of sample size, and that confidence sets are close to being uninformative. In this result the maximum risk is over commonly used specifications for the set of feasible data generating processes. The consequences for inference on unit roots and cointegration are discussed. Similar results for persistence estimation and estimation of the long memory parameter are given. All these results are obtained as special cases of a more general theory developed for abstract estimation problems, which readily also allows for the treatment of other ill‐posed estimation problems such as, e.g., nonparametric regression or density estimation.     

A Geometric Approach to Nonlinear Econometric Models

Conventional tests for composite hypotheses in minimum distance models can be unreliable when the relationship between the structural and reduced‐form parameters is highly nonlinear. Such nonlinearity may arise for a variety of reasons, including weak identification. In this note, we begin by studying the problem of testing a “curved null” in a finite‐sample Gaussian model. Using the curvature of the model, we develop new finite‐sample bounds on the distribution of minimum‐distance statistics. These bounds allow us to construct tests for composite hypotheses which are uniformly asymptotically valid over a large class of data generating processes and structural models.     

A Bayesian Network Estimation of the Service‐Profit Chain for Transport Service Satisfaction

Bayesian network methodology is used to model key linkages of the service‐profit chain within the context of transportation service satisfaction. Bayesian networks offer some advantages for implementing managerially focused models over other statistical techniques designed primarily for evaluating theoretical models. These advantages are (1) providing a causal explanation using observable variables within a single multivariate model, (2) analysis of nonlinear relationships contained in ordinal measurements, (3) accommodation of branching patterns that occur in data collection, and (4) the ability to conduct probabilistic inference for prediction and diagnostics with an output metric that can be understood by managers and academics. Sample data from 1,101 recent transport service customers are utilized to select and validate a Bayesian network and conduct probabilistic inference.     

Inference on Causal Effects in a Generalized Regression Kink Design

We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed assignment variable. We characterize a broad class of models in which a sharp “Regression Kink Design” (RKD or RK Design) identifies a readily interpretable treatment‐on‐the‐treated parameter (Florens, Heckman, Meghir, and Vytlacil (2008)). We also introduce a “fuzzy regression kink design” generalization that allows for omitted variables in the assignment rule, noncompliance, and certain types of measurement errors in the observed values of the assignment variable and the policy variable. Our identifying assumptions give rise to testable restrictions on the distributions of the assignment variable and predetermined covariates around the kink point, similar to the restrictions delivered by Lee (2008) for the regression discontinuity design. Using a kink in the unemployment benefit formula, we apply a fuzzy RKD to empirically estimate the effect of benefit rates on unemployment durations in Austria.