Constant Causal Effects Assumption

Examples

Consider the following example. Assume we want to understand the effect of 4 years of university education versus 0 years of university education on future annual earnings. Suppose further that we were able to conduct a randomized experiment in which some individuals were randomly assigned to receive this education (Group 1) and others were randomized not to receive it (Group 2). If we assumed that the causal effects of education were [Page 219]constant, then we could calculate the effects of a university education by merely comparing the average income of those in Group 1 with those in Group 2. While there may be variance around the mean (i.e., some people within each group make a little more and some a little less), we could calculate some average effect that we would assume to be constant. We could thus make a statement like, “A university education causes an individual's annual income to increase by $40,000 per year, on average.” Problematically, this constant causal effects assumption can be very easily violated. For example, assume that within groups 1 and 2 there are two further evenly sized subgroups (Groups A and B). We now have four subgroups (1A, 1B, 2A, 2B). Now, suppose that the observed annual incomes for each group were as follows. Those in Group 1A earn $100,000 per year. Those in Group 1B earn $40,000 per year. Group 2A and 2B members earn $30,000 per year. The causal effect of a university education appears conditional on whether an individual is a member of Group A or Group B. While the average causal effect of university education still appears to be $40,000 per year, it is in fact quite different for those in Group A and those in Group B. After a more precise measurement of outcomes we would say that a constant causal effects assumption does not hold.

A real-life example of such a finding is that of Joanne Katz, Parul Christian, Francesca Dominici, and Scott Zeger. Katz and colleagues examine the effects of an antenatal micronutrient supplement on the birth weight of infants in rural Nepal. Comparing the average birth weight of those infants that received the nutrients and those that did not, they concluded that prenatal nutrients increase birth weight by 40–70 grams. However, they go a step further to determine whether this treatment effect is constant across infants. Instead, they find that the prenatal nutrients have the most beneficial effects for infants that are the most vulnerable. By looking only at average effects, Katz and colleagues would not have revealed the most beneficial causal effects of this treatment.

...