A Brief History Of Empirical Approaches
Case and Katz (1991) provide a seminal look at the effects of neighborhood peers on risky behaviors and other outcomes, although they are unable to tackle many of the aforementioned empirical issues. In particular, the authors acknowledge that they are unable to control for all environmental confounders and their self-selection into neighborhoods. The authors use what has become a typical empirical framework in the literature:
where, Yig is the health behavior choice of individual i in peer group g (e.g., neighborhood), individual and family characteristics are contained in a vector X, and peer characteristics are measured as group-level averages of the X vector excluding the individual, labeled X-ig . Unobserved factors are contained in the vector, Wg . Finally, Y-ig is the group-level average outcome excluding the individual (e.g., the proportion of individuals in the same neighborhood who report smoking). The main coefficient of interest is the endogenous effect a, which indicates the extent to which individuals are influenced by their peers’ choices. If a is positive, interventions that change the behavior of individuals (or subsets of individuals) within a reference group would be predicted to spillover on nontreated individuals in the same reference group. In addition to acknowledging the potential for omitted group-level variables as well as self-selection (where εig and Y-ig are correlated), the authors are also unable to resolve the simultaneity bias (this issue was not fully discussed until Manski, 1993). The authors find evidence of substantial correlation between own and neighborhood peer substance use, crime, and other behaviors.
Norton et al. (1998) focus on schoolmate peer effects in alcohol and tobacco use of teenagers, and they use an instrumental variables strategy to address the endogeneity of peer groups (see also Evans et al. (1992) for an analysis of teenage pregnancy). Although the focus on endogeneity is important, there is little scope to control for the shared environment due to both data limitations and the instruments (such as neighborhood drug availability and safety) being potentially invalid – in fact, the results have suggested that noninstrumented results are preferable for extremely large peer effects. The general approach of using schoolmates or grademates has been used by many subsequent studies (e.g., Gaviria and Raphael, 2001), wherein too the quality of the instruments are uncertain; specifically, all contextual effects are often assumed to not exist in order to use these variables as instruments.
More recently, Fletcher (2010a) has suggested this approach to be inappropriate and instead proposes a combined instrumental variables/fixed effects design with conceptually appealing diagnostic tests (following Bifulco et al., 2011; Lavy and Schlosser, 2007) in order to validate a preferred instrument set, although the validity of the instruments is still widely questioned. Specifically, Fletcher argues that the increasing proportion of the smoking grademates is due to smoking status of individuals in their households (which can be empirically demonstrated), which does not directly affect respondent smoking even when school-fixed effects are controlled (which is a maintained, untestable assumption). Although Fletcher shows the evidence that exposure of smoking grademates from households of smokers is conditionally random within school, there are ways by which this instrument could be invalidated because, for example, if mothers of grademates are smokers, it simply implies that there is access to tobacco for the respondent. See also Fletcher (2011b) for an examination of peer influences in alcohol consumption.
There have been several alternatives to the instrumental variable approach in the literature. Clark and Loheac (2007) use panel data and a lagged measure of peer behaviors that is combined with school-fixed effects in order to adjust for endogeneity, a large portion of the shared environment, and the reflection problem:
The reflection problem is eliminated because current smoking decisions cannot affect past schoolmate smoking decisions. Although school-fixed effects reduce the issue of contextual effects, a maintained assumption is that, within schools, students choose friends randomly. A second weakness of this design is the need to assume a specific time structure where individual decision making and social influence processes are concerned (e.g., 1 day, 1 week, 1 month, 1 year, 2 years, etc.) (Manski, 1995). Specifically, Manski (1995, p. 136) states, ‘‘Of course, one cannot simply specify a dynamic model and claim that the problem of inference on social effects has been resolved. Dynamic analysis is meaningful only if one has reason to believe that the transmission of social effects follows the assumed temporal pattern.’’
An alternative to implementing a lag structure research design or an instrumental variables strategy is to focus on estimating contextual social effects instead of endogenous social effects. The most convincing work in this area uses random assignment of peers. For example, Kremer and Levy (2008) use data from a university that randomly assigns freshmen to shared dormitory rooms:
where, in this case, X-ig could be thought of as a lagged endogenous social effect examined in some studies or roommate’s precollege alcohol consumption. What allows the estimate to produce a contextual effect rather than an endogenous one is that the individual is not exposed to the actual drinking behavior, but rather is being exposed to having a roommate who has the characteristic of being a past drinker. Additionally, the random assignment of roommates eliminates the concerns regarding the endogeneity of the peer group. Kremer and Levy show that a fresh student who is randomly assigned a roommate with alcoholic past during high school has lower college performance than the student who is assigned a nondrinking roommate. The focus on the roommate’s predetermined high school drinking behavior as the peer effect of interest also eliminates issues of simultaneity bias.
Because not all data sets are able to leverage the random assignment of ‘friends,’ several studies attempt to leverage quasi-random variation in observational data. For example, Bifulco et al. (2011) use a cross-cohort, within-school design to link the outcomes of students to their (quasi-randomly assigned) classmates’ characteristics:
That is, the authors examine the ‘peer effects’ of having a higher share of grademates with educated mothers or a higher share of grademates who are racial/ethnic minorities. This focus on contextual effects sidelines the need for a solution to the reflection problem because student smoking cannot affect grademate race, but some of the important policy issues that are tied to a social multiplier through endogenous peer effects cannot be evaluated directly.