The remuneration of MPs affects who engages in politics. Even if average returns to office are positive, as found in all other studies, some officeholders’ returns are likely negative. Further, the timing of returns to office is crucial as politicians often enjoy delayed compensation like lucrative pensions. Utilizing administrative data for parliamentary candidates in Denmark from 1994 to 2015, we estimate first-time runners’ earnings and total income returns to office. Based on total income, practically all elected MPs experience economic gains during their first term. Computations of life-cycle returns reveal that the 25 percent highest earning candidates (pre-office) have no long-term economic gain from winning. Generally, considering the distribution and timing of returns to office improves studies of how office-holding is economically rewarded.

We construct a framework for meta-analysis and other multi-level data structures that codifies the sources of heterogeneity between studies or settings in treatment effects and examines their implications for analyses. The key idea is to consider, for each of the treatments under investigation, the subject’s potential outcome in each study or setting were he to receive that treatment. We consider four sources of heterogeneity: (1) response inconsistency, whereby a subject’s response to a given treatment would vary across different studies or settings, (2) the grouping of nonequivalent treatments, where two or more treatments are grouped and treated as a single treatment under the incorrect assumption that a subject’s responses to the different treatments would be identical, (3) nonignorable treatment assignment, and (4) response-related variability in the composition of subjects in different studies or settings. We then examine how these sources affect heterogeneity/homogeneity of conditional and unconditional treatment effects. To illustrate the utility of our approach, we re-analyze individual participant data from 29 randomized placebo-controlled studies on the cardiovascular risk of Vioxx, a Cox-2 selective nonsteroidal anti-inflammatory drug approved by the FDA in 1999 for the management of pain and withdrawn from the market in 2004.

Behavioral science researchers have shown strong interest in disaggregating within-person relations from between-person differences (stable traits) using longitudinal data. In this paper, we propose a method of within-person variability score-based causal inference for estimating joint effects of time-varying continuous treatments by controlling for stable traits of persons. After explaining the assumed data-generating process and providing formal definitions of stable trait factors, within-person variability scores, and joint effects of time-varying treatments at the within-person level, we introduce the proposed method, which consists of a two-step analysis. Within-person variability scores for each person, which are disaggregated from stable traits of that person, are first calculated using weights based on a best linear correlation preserving predictor through structural equation modeling (SEM). Causal parameters are then estimated via a potential outcome approach, either marginal structural models (MSMs) or structural nested mean models (SNMMs), using calculated within-person variability scores. Unlike the approach that relies entirely on SEM, the present method does not assume linearity for observed time-varying confounders at the within-person level. We emphasize the use of SNMMs with G-estimation because of its property of being doubly robust to model misspecifications in how observed time-varying confounders are functionally related to treatments/predictors and outcomes at the within-person level. Through simulation, we show that the proposed method can recover causal parameters well and that causal estimates might be severely biased if one does not properly account for stable traits. An empirical application using data regarding sleep habits and mental health status from the Tokyo Teen Cohort study is also provided.

Covariate-adjusted treatment effects are commonly estimated in non-randomized studies. It has been shown that measurement error in covariates can bias treatment effect estimates when not appropriately accounted for. So far, these delineations primarily assumed a true data generating model that included just one single covariate. It is, however, more plausible that the true model consists of more than one covariate. We evaluate when a further covariate may reduce bias due to measurement error in another covariate and in which cases it is not recommended to include a further covariate. We analytically derive the amount of bias related to the fallible covariate’s reliability and systematically disentangle bias compensation and amplification due to an additional covariate. With a fallible covariate, it is not always beneficial to include an additional covariate for adjustment, as the additional covariate can extensively increase the bias. The mechanisms for an increased bias due to an additional covariate can be complex, even in a simple setting of just two covariates. A high reliability of the fallible covariate or a high correlation between the covariates cannot in general prevent from substantial bias. We show distorting effects of a fallible covariate in an empirical example and discuss adjustment for latent covariates as a possible solution.

In the behavioral and social sciences, quasi-experimental and observational studies are used due to the difficulty achieving a random assignment. However, the estimation of differences between groups in observational studies frequently suffers from bias due to differences in the distributions of covariates. To estimate average treatment effects when the treatment variable is binary, Rosenbaum and Rubin (1983a) proposed adjustment methods for pretreatment variables using the propensity score.

However, these studies were interested only in estimating the average causal effect and/or marginal means. In the behavioral and social sciences, a general estimation method is required to estimate parameters in multiple group structural equation modeling where the differences of covariates are adjusted.

We show that a Horvitz-Thompson-type estimator, propensity score weighted M estimator (PWME) is consistent, even when we use estimated propensity scores, and the asymptotic variance of the PWME is shown to be less than that with true propensity scores.

Furthermore, we show that the asymptotic distribution of the propensity score weighted statistic under a null hypothesis is a weighted sum of independent χ12 variables.

We show the method can compare latent variable means with covariates adjusted using propensity scores, which was not feasible by previous methods. We also apply the proposed method for correlated longitudinal binary responses with informative dropout using data from the Longitudinal Study of Aging (LSOA). The results of a simulation study indicate that the proposed estimation method is more robust than the maximum likelihood (ML) estimation method, in that PWME does not require the knowledge of the relationships among dependent variables and covariates.

A central theme of research on human development and psychopathology is whether a therapeutic intervention or a turning-point event, such as a family break-up, alters the trajectory of the behavior under study. This paper lays out and applies a method for using observational longitudinal data to make more confident causal inferences about the impact of such events on developmental trajectories. The method draws upon two distinct lines of research: work on the use of finite mixture modeling to analyze developmental trajectories and work on propensity scores. The essence of the method is to use the posterior probabilities of trajectory group membership from a finite mixture modeling framework, to create balance on lagged outcomes and other covariates established prior to t for the purpose of inferring the impact of first-time treatment at t on the outcome of interest. The approach is demonstrated with an analysis of the impact of gang membership on violent delinquency based on data from a large longitudinal study conducted in Montreal.

Graph-based causal models are a flexible tool for causal inference from observational data. In this paper, we develop a comprehensive framework to define, identify, and estimate a broad class of causal quantities in linearly parametrized graph-based models. The proposed method extends the literature, which mainly focuses on causal effects on the mean level and the variance of an outcome variable. For example, we show how to compute the probability that an outcome variable realizes within a target range of values given an intervention, a causal quantity we refer to as the probability of treatment success. We link graph-based causal quantities defined via the do-operator to parameters of the model implied distribution of the observed variables using so-called causal effect functions. Based on these causal effect functions, we propose estimators for causal quantities and show that these estimators are consistent and converge at a rate of $N^{-1/2}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N^{-1/2}$$\end{document} under standard assumptions. Thus, causal quantities can be estimated based on sample sizes that are typically available in the social and behavioral sciences. In case of maximum likelihood estimation, the estimators are asymptotically efficient. We illustrate the proposed method with an example based on empirical data, placing special emphasis on the difference between the interventional and conditional distribution.

Recently, machine learning (ML) methods have been used in causal inference to estimate treatment effects in order to reduce concerns for model mis-specification. However, many ML methods require that all confounders are measured to consistently estimate treatment effects. In this paper, we propose a family of ML methods that estimate treatment effects in the presence of cluster-level unmeasured confounders, a type of unmeasured confounders that are shared within each cluster and are common in multilevel observational studies. We show through simulation studies that our proposed methods are robust from biases from unmeasured cluster-level confounders in a variety of multilevel observational studies. We also examine the effect of taking an algebra course on math achievement scores from the Early Childhood Longitudinal Study, a multilevel observational educational study, using our methods. The proposed methods are available in the CURobustML R package.

Due to the difficulty in achieving a random assignment, a quasi-experimental or observational study design is frequently used in the behavioral and social sciences. If a nonrandom assignment depends on the covariates, multiple group structural equation modeling, that includes the regression function of the dependent variables on the covariates that determine the assignment, can provide reasonable estimates under the condition of correct specification of the regression function. However, it is usually difficult to specify the correct regression function because the dimensions of the dependent variables and covariates are typically large. Therefore, the propensity score adjustment methods have been proposed, since they do not require the specification of the regression function and have been applied to several applied studies. However, these methods produce biased estimates if the assignment mechanism is incorrectly specified. In order to make a more robust inference, it would be more useful to develop an estimation method that integrates the regression approach with the propensity score methodology. In this study we propose a doubly robust-type estimation method for marginal multiple group structural equation modeling. This method provides a consistent estimator if either the regression function or the assignment mechanism is correctly specified. A simulation study indicates that the proposed estimation method is more robust than the existing methods.

Quantifying the causal effects of race is one of the more controversial and consequential endeavors to have emerged from the causal revolution in the social sciences. The predominant view within the causal inference literature defines the effect of race as the effect of race perception and commonly equates this effect with “disparate treatment” racial discrimination. If these concepts are indeed equivalent, the stakes of these studies are incredibly high as they stand to establish or discredit claims of discrimination in courts, policymaking circles and public opinion. This paper interrogates the assumptions upon which this enterprise has been built. We ask: what is a perception of race, a perception of, exactly? Drawing on a rich tradition of work in critical race theory and social psychology on racial cognition, we argue that perception of race and perception of other decision-relevant features of an action situation are often co-constituted; hence, efforts to distinguish and separate these effects from each other are theoretically misguided. We conclude that empirical studies of discrimination must turn to defining what constitutes just treatment in light of the social differences that define race.

Synthetic controls (SCs) are widely used to estimate the causal effect of a treatment. However, they do not account for the different speeds at which units respond to changes. Reactions may be inelastic or “sticky” and thus slower due to varying regulatory, institutional, or political environments. We show that these different reaction speeds can lead to biased estimates of causal effects. We therefore introduce a dynamic SC approach that accommodates varying speeds in time series, resulting in improved SC estimates. We apply our method to re-estimate the effects of terrorism on income (Abadie and Gardeazabal [2003, American Economic Review 93, 113–132]), tobacco laws on consumption (Abadie, Diamond, and Hainmueller [2010, Journal of the American Statistical Association 105, 493–505]), and German reunification on GDP (Abadie, Diamond, and Hainmueller [2015, American Journal of Political Science 59, 495–510]). We also assess the method’s performance using Monte Carlo simulations. We find that it reduces errors in the estimates of true treatment effects by up to 70% compared to traditional SCs, improving our ability to make robust inferences. An open-source R package, dsc, is made available for easy implementation.