Conditioning on Post-treatment Variables

Pearl, Judea

doi:10.1515/jci-2015-0005

Cited by 7 publications

(7 citation statements)

References 4 publications

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“…One reason why we have not detected any strong e ects may be due to the identi cation strategy authors use in their models. On the one hand, OLS and panel data models require too many controls to make units comparable, and they are vulnerable to omitted variable bias or post-treatment bias (Cinelli and Hazlett 2020;Pearl 2015). On the other hand, estimation methods such as instrumental variables and regression discontinuity designs have become popular because of their high internal validity (Angrist and Pischke 2008).…”

Section: Meta-analysismentioning

confidence: 99%

The Effect of Legislature Size on Public Spending: A Meta-Analysis

Alptekin¹,

Freire²,

Mignozzetti³

et al. 2020

Preprint

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In a seminal article, Weingast et al. (1981) argue that there is a positive relationship between legislature size and inefficiency in public expenditures. Their proposition is currently known as the "law of _1/n_" and has been widely cited by scholars in political science and public administration. However, recent studies have questioned the validity of the theory. In this paper, we estimate the first meta-analysis of the relationship between the number of legislators and public spending. Based on a sample of 26 empirical studies, we find little effect of legislature size on government budgets. The available evidence suggests that, if such an effect exists, it is driven by an increase in the upper chamber, but there is considerable heterogeneity in the results. Our meta-regressions also indicate that study coefficients vary significantly according to modelling specifications, such as estimation method or variable selection.

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Section: Meta-analysismentioning

confidence: 99%

The Effect of Legislature Size on Public Spending: A Meta-Analysis

Alptekin¹,

Freire²,

Mignozzetti³

et al. 2020

Preprint

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“…73-74, 11, 12]; but has become extremely useful in graphical analysis. The difference between the conditioning operators used in these two frameworks is reflected in the difference between the counterfactual expression PðY x ¼ yjzÞ and the do-expression PðY ¼ yjdoðX ¼ xÞ; zÞ [13]. The latter expression defines information that is estimable directly from experimental studies, whereas the former invokes retrospective counterfactuals that may or may not be estimable empirically.…”

Section: Transportability and Selection Biasmentioning

confidence: 99%

“…Moreover, even when S-ignorability holds, eq. (5) would only be applicable if the factor Pðy x jS ¼ 1; zÞ is estimable in the experimental study and this will generally not be the case when Z contains post-treatment variables (see [13], Figure 1). …”

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confidence: 99%

Generalizing Experimental Findings

Pearl

2015

Journal of Causal Inference

Self Cite

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This note examines one of the most crucial questions in causal inference: "How generalizable are randomized clinical trials?" The question has received a formal treatment recently, using a non-parametric setting, and has led to a simple and general solution. I will describe this solution and several of its ramifications, and compare it to the way researchers have attempted to tackle the problem using the language of ignorability. We will see that ignorability-type assumptions need to be enriched with structural assumptions in order to capture the full spectrum of conditions that permit generalizations, and in order to judge their plausibility in specific applications.Keywords: generalizability, transportability, selection bias, admissibility, ignorability Transportability and selection biasThe long-standing problem of generalizing experimental findings from the trial sample to the population as a whole, also known as the problem of "sample selection-bias" [1,2], has received renewed attention in the past decade, as more researchers come to recognize this bias as a major threat to the validity of experimental findings in both the health sciences [3] and social policy making [4]. Since participation in a randomized trial cannot be mandated, we cannot guarantee that the study population would be the same as the population of interest. For example, the study population may consist of volunteers, who respond to financial and medical incentives offered by pharmaceutical firms or experimental teams, so, the distribution of outcomes in the study may differ substantially from the distribution of outcomes under the policy of interest.Another impediment to the validity of experimental finding is that the types of individuals in the target population may change over time [5]. For example, as more individuals become eligible for health insurance, the types of individuals seeking services would no longer match the type of individuals that were sampled for the study [3]. A similar change would occur as more individuals become aware of the efficacy of the treatment. The result is an inherent disparity between the target population and the population under study.The problem of generalizing across disparate populations has received a formal treatment in Pearl and Bareinboim [6] where it was labeled "transportability," and where necessary and sufficient conditions for valid generalization were established (see [7]). The problem of selection bias, though it has some unique features, can also be viewed as a nuance of the transportability problem, thus inheriting all the theoretical results established in Pearl and Bareinboim [6] that guarantee valid generalizations. I will describe the two problems side by side and then return to the distinction between the type of assumptions that are needed for enabling generalizations.The transportability problem concerns two dissimilar populations, Å and Å Ã , and requires us to estimate the average causal effect P Ã ðy x Þ (explicitly: The first two components of I TR represent, resp...

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“…The difference between the conditioning operators used in these two frameworks is reflected in the difference between the counterfactual expression P (Y x = y|z) and the do-expression P (Y = y|do(X = x), z). (Pearl, 2015). The latter expression defines information that is estimable directly from experimental studies, whereas the former invokes retrospective counterfactuals that may or may not be estimable empirically.…”

Section: Transportability and Selection Biasmentioning

confidence: 99%