Statistical Science 2010, Vol. 25, No. 1, 51–71 DOI: 10.1214/10-STS321 © Institute of Mathematical Statistics, 2010 Identification, Inference and Sensitivity Analysis for Causal Mediation Effects Kosuke Imai, Luke Keele and Teppei Yamamoto Abstract. Causal mediation analysis is routinely conducted by applied re- searchers in a variety of disciplines. The goal of such an analysis is to inves- tigate alternative causal mechanisms by examining the roles of intermediate variables that lie in the causal paths between the treatment and outcome vari- ables. In this paper we first prove that under a particular version of sequen- tial ignorability assumption, the average causal mediation effect (ACME) is nonparametrically identified. We compare our identification assumption with those proposed in the literature. Some practical implications of our identifi- cation result are also discussed. In particular, the popular estimator based on the linear structural equation model (LSEM) can be interpreted as an ACME estimator once additional parametric assumptions are made. We show that these assumptions can easily be relaxed within and outside of the LSEM framework and propose simple nonparametric estimation strategies. Second, and perhaps most importantly, we propose a new sensitivity analysis that can be easily implemented by applied researchers within the LSEM framework. Like the existing identifying assumptions, the proposed sequential ignorabil- ity assumption may be too strong in many applied settings. Thus, sensitivity analysis is essential in order to examine the robustness of empirical findings to the possible existence of an unmeasured confounder. Finally, we apply the proposed methods to a randomized experiment from political psychol- ogy. We also make easy-to-use software available to implement the proposed methods. Key words and phrases: Causal inference, causal mediation analysis, direct and indirect effects, linear structural equation models, sequential ignorability, unmeasured confounders. 1. INTRODUCTION such an analysis is to investigate causal mechanisms by examining the role of intermediate variables thought to Causal mediation analysis is routinely conducted by lie in the causal path between the treatment and out- applied researchers in a variety of scientific disciplines come variables. Over fifty years ago, Cochran (1957) including epidemiology, political science, psychology pointed to both the possibility and difficulty of using and sociology (see MacKinnon, 2008). The goal of covariance analysis to explore causal mechanisms by stating: “Sometimes these averages have no physical Kosuke Imai is Assistant Professor, Department of Politics, or biological meaning of interest to the investigator, Princeton University, Princeton, New Jersey 08544, USA and sometimes they do not have the meaning that is (e-mail: [email protected];URL: http://imai.princeton.edu). Luke Keele is Assistant ascribed to them at first glance” (page 267). Recently, Professor, Department Political Science, Ohio State a number of statisticians have taken up Cochran’s chal- University, 2140 Derby Hall, Columbus, Ohio 43210, USA lenge. Robins and Greenland (1992) initiated a formal (e-mail: [email protected]). Teppei Yamamoto is study of causal mediation analysis, and a number of ar- Ph.D. Student, Department of Politics, Princeton ticles have appeared in more recent years (e.g., Pearl, University, 031 Corwin Hall, Princeton, New Jersey 08544, 2001; Robins, 2003; Rubin, 2004; Petersen, Sinisi and USA (e-mail: [email protected]). van der Laan, 2006; Geneletti, 2007;Joffe,Smalland 51 52 K. IMAI, L. KEELE AND T. YAMAMOTO Hsu, 2007; Ten Have et al., 2007; Albert, 2008;Jo, that the sequential ignorability assumption cannot be 2008; Joffe et al., 2008; Sobel, 2008; VanderWeele, directly tested even in randomized experiments, sen- 2008, 2009; Glynn, 2010). sitivity analysis must play an essential role in causal What do we mean by a causal mechanism? The mediation analysis. Finally, in Section 6 we apply the aforementioned paper by Cochran gives the follow- proposed methods to the empirical example, to which ing example. In a randomized experiment, researchers we now turn. study the causal effects of various soil fumigants on eelworms that attack farm crops. They observe that 2. AN EXAMPLE FROM THE SOCIAL SCIENCES these soil fumigants increase oats yields but wish to know whether the reduction of eelworms represents Since the influential article by Baron and Kenny an intermediate phenomenon that mediates this effect. (1986), mediation analysis has been frequently used In fact, many scientists across various disciplines are in the social sciences and psychology in particular. not only interested in causal effects but also in causal A central goal of these disciplines is to identify causal mechanisms because competing scientific theories of- mechanisms underlying human behavior and opinion ten imply that different causal paths underlie the same formation. In a typical psychological experiment, re- cause-effect relationship. searchers randomly administer certain stimuli to sub- In this paper we contribute to this fast-growing lit- jects and compare treatment group behavior or opin- erature in several ways. After briefly describing our ions with those in the control group. However, to di- motivating example in the next section, we prove in rectly test psychological theories, estimating the causal Section 3 that under a particular version of the sequen- effects of the stimuli is typically not sufficient. Instead, tial ignorability assumption, the average causal media- researchers choose to investigate psychological factors tion effect (ACME) is nonparametrically identified. We such as cognition and emotion that mediate causal ef- compare our identifying assumption with those pro- fects in order to explain why individuals respond to a posed in the literature, and discuss practical implica- certain stimulus in a particular way. Another difficulty tions of our identification result. In particular, Baron faced by many researchers is their inability to directly and Kenny’s (1986) popular estimator (Google Scholar manipulate psychological constructs. It is in this con- records over 17 thousand citations for this paper), text that causal mediation analysis plays an essential which is based on a linear structural equation model role in social science research. (LSEM), can be interpreted as an ACME estimator un- In Section 6 we apply our methods to an influen- der the proposed assumption if additional parametric tial randomized experiment from political psychology. assumptions are satisfied. We show that these addi- Nelson, Clawson and Oxley (1997) examine how the tional assumptions can be easily relaxed within and framing of political issues by the news media affects outside of the LSEM framework. In particular, we pro- citizens’ political opinions. While the authors are not pose a simple nonparametric estimation strategy in the first to use causal mediation analysis in political Section 4. We conduct a Monte Carlo experiment to science, their study is one of the most well-known ex- investigate the finite-sample performance of the pro- amples in political psychology and also represents a posed nonparametric estimator and its asymptotic con- typical application of causal mediation analyses in the fidence interval. social sciences. Media framing is the process by which Like many identification assumptions, the proposed news organizations define a political issue or empha- assumption may be too strong for the typical situations size particular aspects of that issue. The authors hy- in which causal mediation analysis is employed. For pothesize that differing frames for the same news story example, in experiments where the treatment is ran- alter citizens’ political tolerance by affecting more gen- domized but the mediator is not, the ignorability of the eral political attitudes. They conducted a randomized treatment assignment holds but the ignorability of the experiment to test this mediation hypothesis. mediator may not. In Section 5 we propose a new sen- Specifically, Nelson, Clawson and Oxley (1997) sitivity analysis that can be implemented by applied re- used two different local newscasts about a Ku Klux searchers within the standard LSEM framework. This Klan rally held in central Ohio. In the experiment, method directly evaluates the robustness of empirical student subjects were randomly assigned to watch the findings to the possible existence of unmeasured pre- nightly news from two different local news channels. treatment variables that confound the relationship be- The two news clips were identical except for the final tween the mediator and the outcome. Given the fact story on the Klan rally. In one newscast, the Klan rally CAUSAL MEDIATION ANALYSIS 53 was presented as a free speech issue. In the second than various causal effects given in the last column of newscast, the journalists presented the Klan rally as a Table 1. Indeed, in many social science experiments, disruption of public order that threatened to turn vio- researchers’ interest lies in the identification of causal lent. The outcome was measured using two different mediation effects rather than the total causal effect or scales of political tolerance. Immediately after viewing controlled direct effects (these terms are formally de- the news broadcast, subjects were asked two seven- fined in the next section). Causal mediation analysis is point scale questions measuring their tolerance for the particularly appealing