In his extension of the identification problem to the social sciences, Charles Manski, in his book Identification Problems in the Social Sciences (1995), poses the reflection problem. The problem surfaces when one tries to predict the behavior of an individual by the behavior of the group of which the individual is a member. The problem is likened to the image of a person reflected in a mirror. The mirror can be said to reflect the image of the person’s motion or to reflect the image and the person moving together consequent to an external stimulus.
The reflection problem is further explained through the variables used in a statistical model. Standard identification problems in economics use observations of prices and quantities, two endogenous variables, to reveal consumers’ and producers’ behavior. The economist would add predetermined variables to identify the demand and supply curves. The reflection problem, however, looks at other endogenous effects that are overlooked or ignored in the standard order-and-rank identification process in economics. These additional variables are used mostly by sociologists who are concerned with how problems are reflected from society to the individual, while economists usually use social effects as constraints of individual opportunities.
Modern researchers are unable to solve the reflection problem through the modeling of output data, which cannot capture the reflection problem. One of their hypotheses might be that individuals belonging to a group tend to behave similarly. The researchers probe their models for endogenous, contextual, and correlated effects. Models with endogenous effects explain variations in individual behavior by the prevalence of the behavior in a group. Individuals behave similarly because they may experience pressure to conform to certain norms. Models of contextual effects explain individual behavior with the variation of background characteristics of the group, such as the influence of the neighborhood environment. Models of correlated effects assess whether individuals facing a similar environment or sharing similar individual characteristics will behave the same way. For example, people may associate with each other because they share similar characteristics.
Manski provides an intuitive example to explain the problem of separating these effects. A measure of the mean behavior of the group will contain the individual behavior. A measure of the outcome of a group behavior might simply be an aggregation of individual behaviors. One cannot be sure, therefore, that it reveals the individual behavior. By using the mean behavior of a group, the mean value of exogenous attributes of a group, or similar characteristics of members of a group to explain individual behavior, one captures exogenous, contextual, and correlated effects, respectively. To infer individual behavior from a measure of group behavior would require prior information that explains the composition of the group. To distinguish among these effects, it is necessary to know something more about how the groups are formed and how the members interact.
One can solve the reflection problem if one knows that the group mean influences individual behavior with a specific lag structure. Analogous assertions can be made if the researchers know a nonlinear specification, specific group features, or some instrument that conveys influences from the group to the individual. Generally, such information is not available.
SEE ALSO Behaviorism; General Linear Model; Identification Problem; Least Squares, Ordinary; Nonlinear Regression; Structural Equation Models
Manski, Charles F. 1993. Identification of Endogenous Social Effects: The Reflection Problem. Review of Economic Studies 60 (3): 531-542.
Manski, Charles F. 1995. Identification Problems in the Social Sciences. Cambridge, MA: Harvard University Press.
Manski, Charles F. 2003. Identification Problems in the Social Sciences and Everyday Life. Southern Economic Journal 70 (1): 11-21.