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Counterfactuals and causal inference : methods and principles for social research
\"In this second edition of Counterfactuals and Causal Inference, completely revised and expanded, the essential features of the counterfactual approach to observational data analysis are presented with examples from the social, demographic, and health sciences. Alternative estimation techniques are first introduced using both the potential outcome model and causal graphs; after which, conditioning techniques, such as matching and regression, are presented from a potential outcomes perspective. For research scenarios in which important determinants of causal exposure are unobserved, alternative techniques, such as instrumental variable estimators, longitudinal methods, and estimation via causal mechanisms, are then presented. The importance of causal effect heterogeneity is stressed throughout the book, and the need for deep causal explanation via mechanisms is discussed\"-- Provided by publisher.
Book
Analyzing Age-Period-Cohort Data: A Review and Critique
Age-period-cohort (APC) analysis has a long, controversial history in sociology and related fields. Despite the existence of hundreds, if not thousands, of articles and dozens of books, there is little agreement on how to adequately analyze APC data. This article begins with a brief overview of APC analysis, discussing how one can interpret APC effects in a causal way. Next, we review methods that obtain point identification of APC effects, such as the equality constraints model, Moore-Penrose estimators, and multilevel models. We then outline techniques that entail point identification using measured causes, such as the proxy variables approach and mechanism-based models. Next, we discuss a general framework for APC analysis grounded in partial identification using bounds and sensitivity analyses. We conclude by outlining a general step-by-step procedure for conducting APC analyses, presenting an empirical example examining temporal shifts in verbal ability.
Journal Article
Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable
Endogenous selection bias is a central problem for causal inference. Recognizing the problem, however, can be difficult in practice. This article introduces a purely graphical way of characterizing endogenous selection bias and of understanding its consequences (Hernán et al. 2004). We use causal graphs (direct acyclic graphs, or DAGs) to highlight that endogenous selection bias stems from conditioning (e.g., controlling, stratifying, or selecting) on a so-called collider variable, i.e., a variable that is itself caused by two other variables, one that is (or is associated with) the treatment and another that is (or is associated with) the outcome. Endogenous selection bias can result from direct conditioning on the outcome variable, a post-outcome variable, a post-treatment variable, and even a pre-treatment variable. We highlight the difference between endogenous selection bias, common-cause confounding, and overcontrol bias and discuss numerous examples from social stratification, cultural sociology, social network analysis, political sociology, social demography, and the sociology of education.
Journal Article
The Gains of Greater Granularity
Objectives
This study applies the growing emphasis on micro-places to the analysis of addresses, assessing the presence and persistence of “problem properties” with elevated levels of crime and disorder. It evaluates what insights this additional detail offers beyond the analysis of neighborhoods and street segments.
Methods
We used over 2,000,000 geocoded emergency and non-emergency requests received by the City of Boston’s 911 and 311 systems from 2011–2013 to calculate six indices of violent crime, physical disorder, and social disorder for all addresses (
n
= 123,265). We linked addresses to their street segment (
n
= 13,767) and census tract (
n
= 178), creating a three-level hierarchy that enabled a series of multilevel Poisson hierarchical models.
Results
Less than 1% of addresses generated 25% of reports of crime and disorder. Across indices, 95–99% of variance was at the address level, though there was significant clustering at the street segment and neighborhood levels. Models with lag predictors found that levels of crime and disorder persisted across years for all outcomes at all three geographic levels, with stronger effects at higher geographic levels. Distinctively, ~15% of addresses generated crime or disorder in one year and not in the other.
Conclusions
The analysis suggests new opportunities for both the criminology of place and the management of public safety in considering addresses in conjunction with higher-order geographies. We explore directions for empirical work including the further experimentation with and evaluation of law enforcement policies targeting problem properties.
Journal Article
Multicollinearity and Model Misspecification
Multicollinearity in linear regression is typically thought of as a problem of large standard errors due to near-linear dependencies among independent variables. This problem can be solved by more informative data, possibly in the form of a larger sample. We argue that this understanding of multicollinearity is only partly correct. The near collinearity of independent variables can also increase the sensitivity of regression estimates to small errors in the model misspecification. We examine the classical assumption that independent variables are uncorrelated with the errors. With collinearity, small deviations from this assumption can lead to large changes in estimates. We present a Bayesian estimator that specifies a prior distribution for the covariance between the independent variables and the error term. This estimator can be used to calculate confidence intervals that reflect sampling error and uncertainty about the model specification. A Monte Carlo experiment indicates that the Bayesian estimator has good frequentist properties in the presence of specification errors. We illustrate the new method by estimating a model of the black-white gap in earnings.
Journal Article
Bounding Analyses of Age-Period-Cohort Effects
For more than a century, researchers from a wide range of disciplines have sought to estimate the unique contributions of age, period, and cohort (APC) effects on a variety of outcomes. A key obstacle to these efforts is the linear dependence among the three time scales. Various methods have been proposed to address this issue, but they have suffered from either ad hoc assumptions or extreme sensitivity to small differences in model specification. After briefly reviewing past work, we outline a new approach for identifying temporal effects in population-level data. Fundamental to our framework is the recognition that it is only the slopes of an APC model that are unidentified, not the nonlinearities or particular combinations of the linear effects. One can thus use constraints implied by the data along with explicit theoretical claims to bound one or more of the APC effects. Bounds on these parameters may be nearly as informative as point estimates, even with relatively weak assumptions. To demonstrate the usefulness of our approach, we examine temporal effects in prostate cancer incidence and homicide rates. We conclude with a discussion of guidelines for further research on APC effects.
Journal Article
Cross-Group Differences in Age, Period, and Cohort Effects: A Bounding Approach to the Gender Wage Gap
For decades, researchers have sought to understand the separate contributions of age, period, and cohort (APC) on a wide range of outcomes. However, a major challenge in these efforts is the linear dependence among the three time scales. Previous methods have been plagued by either arbitrary assumptions or extreme sensitivity to small variations in model specification. In this article, we present an alternative method that achieves partial identification by leveraging additional information about subpopulations (or strata) such as race, gender, and social class. Our first goal is to introduce the cross-strata linearized APC (CSL-APC) model, a re-parameterization of the traditional APC model that focuses on cross-group variations in effects instead of overall effects. Similar to the traditional model, the linear cross-strata APC effects are not identified. The second goal is to show how Fosse and Winship's (2019) bounding approach can be used to address the identification problem of the CSL-APC model, allowing one to partially identify cross-group differences in effects. This approach often involves weaker assumptions than previously used techniques and, in some cases, can lead to highly informative bounds. To illustrate our method, we examine differences in temporal effects on wages between men and women in the United States.
Journal Article
Moore–Penrose Estimators of Age–Period–Cohort Effects: Their Interrelationship and Properties
The intrinsic estimator (IE) has become a widely used tool for the analysis of age–period–cohort (APC) data in sociology, demography, and other fields. However, it has been recently recognized that the IE is a subtype of a larger class of estimators based on the Moore–Penrose generalized inverse (MP estimators) and that different estimators can lead to radically divergent estimates of the true, unknown APC effects. To clarify the differences and similarities of MP estimators, we introduce a canonical form of the linear constraints imposed on the true temporal effects. Using this canonical form, we compare the IE to related MP estimators, examining the conditions under which they recover the true temporal effects, the impact of the size and sign of nonlinearities on the estimated linear effects, and their sensitivity to the number of age, period, and cohort categories. We show that two MP estimators, which we call the difference estimator (DE) and the orthogonal estimator (OE), impose constraints that are both less sensitive and easier to interpret than those of the IE. We conclude with practical guidelines for researchers interested in using MP estimators to estimate temporal effects.
Journal Article
The Estimation of Causal Effects from Observational Data
When experimental designs are infeasible, researchers must resort to the use of observational data from surveys, censuses, and administrative records. Because assignment to the independent variables of observational data is usually nonrandom, the challenge of estimating causal effects with observational data can be formidable. In this chapter, we review the large literature produced primarily by statisticians and econometricians in the past two decades on the estimation of causal effects from observational data. We first review the now widely accepted counterfactual framework for the modeling of causal effects. After examining estimators, both old and new, that can be used to estimate causal effects from cross-sectional data, we present estimators that exploit the additional information furnished by longitudinal data. Because of the size and technical nature of the literature, we cannot offer a fully detailed and comprehensive presentation. Instead, we present only the main features of methods that are accessible and potentially of use to quantitatively oriented sociologists.
Journal Article