Controlling for individual differences when variable of interest is time invariate to the individual

Question

I have been thinking through an analysis that asks the question: how do young versus old consumers purchasing differ in response to media coverage of a firm's product.

I have a large random set of data of consumer good purchases for individuals in Ireland. I then collected information about news coverage for each firm in the data.

Let us assume that anyone under 25 is "young." The obvious analysis I ran was a regression of purchases on this dichotomous variable interacted with media coverage.

I want to account for individual differences and thought an easy way to do this is a fixed effect for each individual. Since it is only 11 months of data, no one crosses the threshold from young = 0 to young = 1 so I cannot run this regression. I did run a subsample regression that removes all of the young (or old) and could now include these fixed effects to do a regression of purchase on media. This does not seem like the right way to do this.

My worry is that the main effect from my first regression is being driven by some individual differences and not necessarily being old or young and I want to control for this. Is there a way to handle this scenario apart from fixed effects?

Answer 1

I am assuming the individual's age in your model is time invariant, thus, you will not be able to use fixed effects. This is important because since an individual does not experience both being "young" and "old" you cannot estimate any within person differences. Furthermore, a random effect is also not that helpful since you observe each person in your sample, and it is not a subset of the greater sample so you do not care to estimate random effects. What you can do is control for any parameter that you think is driving a person-level effect and then use your age indicator in an interaction term in your model. This will tell you how the average young/old person reacts.