1
Introduction

According to an ancient Chinese fable, a farmer who was eager to help his crops grow went into his field and pulled each seedling upward. After exhausting himself with the work, he announced to his family that they were going to have a good harvest, only to find the next morning that the plants had wilted and died. Readers with minimal agricultural knowledge may immediately point out the following: the farmer's intervention theory was based on a correct observation that crops that grow taller tend to produce more yield. Yet his hypothesis reflects a false understanding of the cause and the effect-that seedlings pulled to be taller would yield as much as seedlings thriving on their own.

In their classic Design and Analysis of Experiments, Hinkelmann and Kempthorne (1994; updated version of Kempthorne, 1952) discussed two types of science: descriptive science and the development of theory. These two types of science are interrelated in the following sense: observations of an event and other related events, often selected and classified for description by scientists, naturally lead to one or more explanations that we call "theoretical hypotheses," which are then screened and falsified by means of further observations, experimentation, and analyses (Popper, 1963). The experiment of pulling seedlings to be taller was costly, but did serve the purpose of advancing this farmer's knowledge of "what does not work." To develop a successful intervention, in this case, would require a series of empirical tests of explicit theories identifying potential contributors to crop growth. This iterative process gradually deepens our knowledge of the relationships between supposed causes and effects-that is, causality-and may eventually increase the success of agricultural, medical, and social interventions.

1.1 Concepts of moderation, mediation, and spill-over

Although the story of the ancient farmer is fictitious, numerous examples can be found in the real world in which well-intended interventions fail to produce the intended benefits or, in many cases, even lead to unintended consequences. "Interventions" and "treatments," used interchangeably in this book, broadly refer to actions taken by agents or circumstances experienced by an individual or groups of individuals. Interventions are regularly seen in education, physical and mental health, social services, business, politics, and law enforcement. In an education intervention, for example, teachers are typically the agents who deliver a treatment to students, while the impact of the treatment on student outcomes is of ultimate causal interest. Some educational practices such as "teaching to the test" have been criticized to be nearly as counterproductive as the attempt of helping seedlings grow by pulling them upward. "Interventions" and "treatments" under consideration do not exclude undesired experiences such as exposure to poverty, abuse, crime, or bereavement. A treatment, planned or unplanned, becomes a focus of research if there are theoretical reasons to anticipate its impact, positive or negative, on the well-being of individuals who are embedded in social settings including families, classrooms, schools, neighborhoods, and workplaces.

In social science research in general and in policy and program evaluations in particular, questions concerning whether an intervention works and, if so, which version of the intervention works, for whom, under what conditions, and why are key to the advancement of scientific and practical knowledge. Although most empirical investigations in the social sciences concentrate on the average effect of a treatment for a specific population as opposed to the absence of such a treatment (i.e., the control condition), in-depth theoretical reasoning with regard to how the causal effect is generated, substantiated by compelling empirical evidence, is crucial for advancing scientific understanding.

First, when there are multiple versions or different dosages of the treatment or when there are multiple versions of the control condition, a binary divide between "the treatment" and "the control" may not be as informative as fine-grained comparisons across, for example, "treatment version A," "treatment version B," "control version A," and "control version B." For example, expanding the federally funded Head Start program to poor children is expected to generate a greater benefit when few early childhood education alternatives are available (call it "control version A") than when there is an abundance of alternatives including state-sponsored preschool programs (call it "control version B").

Second, the effect of an intervention will likely vary among individuals or across social settings. A famous example comes from medical research: the well-publicized cardiovascular benefits of initiating estrogen therapy during menopause were contradicted later by experimental findings that the same therapy increased postmenopausal women's risk for heart attacks. The effect of an intervention may also depend on the provision of some other concurrent or subsequent interventions. Such heterogeneous effects are often characterized as moderated effects in the literature.

Third, alternative theories may provide competing explanations for the causal mechanisms, that is, the processes through which the intervention produces its effect. A theoretical construct characterizing the hypothesized intermediate process is called a mediator of the intervention effect. The fictitious farmer never developed an elaborate theory as to what caused some seedlings to surpass others in growth. Once scientists revealed the causal relationship between access to chemical nutrients in soil and plant growth, wide applications of chemically synthesized fertilizers finally led to a major increase in crop production.

Finally, it is well known in agricultural experiments that a new type of fertilizer applied to one plot may spill-over to the next plot. Because social connections among individuals are prevalent within organizations or through networks, an individual's response to the treatment may similarly depend on the treatment for other individuals in the same social setting, which may lead to possible spill-overs of intervention effects among individual human beings.

Answering questions with regard to moderation, mediation, and spill-over poses major conceptual and analytic challenges. To date, psychological research often presents well-articulated theories of causal mechanisms relating stimuli to responses. Yet, researchers often lack rigorous analytic strategies for empirically screening competing theories explaining the observed effect. Sociologists have keen interest in the spill-over of treatment effects transmitted through social interactions yet have produced limited evidence quantifying such effects. As many have pointed out, in general, terminological ambiguity and conceptual confusion have been prevalent in the published applied research (Holmbeck, 1997; Kraemer et al., 2002, 2008).

A new framework for conceptualizing moderated, mediated, and spill-over effects has emerged relatively recently in the statistics and econometrics literature on causal inference (e.g., Abbring and Heckman, 2007; Frangakis and Rubin, 2002; Heckman and Vytlacil, 2007a, b; Holland, 1988; Hong and Raudenbush, 2006; Hudgens and Halloran, 2008; Jo, 2008; Pearl, 2001; Robins and Greenland, 1992; Sobel, 2008). The potential for further conceptual and methodological development and for broad applications in the field of behavioral and social sciences promises to greatly advance the empirical basis of our knowledge about causality in the social world.

This book clarifies theoretical concepts and introduces innovative statistical strategies for investigating the average effects of multivalued treatments, moderated treatment effects, mediated treatment effects, and spill-over effects in experimental or quasiexperimental data. Defining individual-specific and population average treatment effects in terms of potential outcomes, the book relates the mathematical forms to the substantive meanings of moderated, mediated, and spill-over effects in the context of application examples. It also explicates and evaluates identification assumptions and contrasts innovative statistical strategies with conventional analytic methods.

1.1.1 Moderated treatment effects

It is hard to accept the assumption that a treatment would produce the same impact for every individual in every possible circumstance. Understanding the heterogeneity of treatment effects therefore is key to the development of causal theories. For example, some studies reported that estrogen therapy improved cardiovascular health among women who initiated its use during menopause. According to a series of other studies, however, the use of estrogen therapy increased postmenopausal women's risk for heart attacks (Grodstein et al., 1996, 2000; Writing Group for the Women's Health Initiative Investigators, 2002). The sharp contrast of findings from these studies led to the hypothesis that age of initiation moderates the effect of estrogen therapy on women's health (Manson and Bassuk, 2007; Rossouw et al., 2007). Revelations of the moderated causal relationship greatly enrich theoretical...