Identification of Endogenous Social Effects: The Reflection Problem

TLDR

The study investigates the reflection problem that arises when researchers attempt to infer group‑level influence on individual behavior from observed population behavior distributions. Inference is only possible with prior knowledge of reference group composition; otherwise it is impossible, and success depends on the functional or statistical relationship between reference group variables and outcome variables, being best when they are moderately related.

Abstract

This paper examines the reflection problem that arises when a researcher observing the distribution of behaviour in a population tries to infer whether the average behaviour in some group influences the behaviour of the individuals that comprise the group. It is found that inference is not possible unless the researcher has prior information specifying the compisition of reference groups. If this information is available, the prospects for inference depend critically on the population relationship between the variables defining reference groups and those directly affecting outcomes. Inference is difficult to implossible if these variables are functionally dependent or are statistically independent. The prospects are better if the variables defining reference groups and those directly affecting outcomes are moderately related in the population.