1
$\begingroup$

I am reading a paper and it has the following simple model: Y = a + b1 + b2 + b1*b2 + e. The author seems to be interested in b1, not the interaction term. How do we interpret b1 in this case? I'm a little confused because most people would be interested in the interaction effect. By including the interaction term as a control variable, how does our interpretation of b1 change?

Thank you!

Improve this question
$\endgroup$

1 Answer 1

Reset to default
2
$\begingroup$

The coefficient on b1 corresponds to the change in the expected value of the outcome for a unit increase in b1 when b2 = 0. If b2 being 0 is meaningless or uninformative, then the coefficient on b1 will be meaningless as well.

Often people center b2 at its mean, so that when the centered version is 0, the original variable is at its mean. This gives a nice interpretation for the coefficient on b1: the change in the expected value of the outcome for a unit increase in b1 when b2 is at its mean (i.e., when centered b2 is 0).

When the interaction is included (whether b2 is centered or not), each individual has a different value of the slope of b1 on Y. If you were to take the average of these slopes, you get a summary measure that some would consider something like the "main effect" of b1. It turns out that in a linear model, this averaged slope is equal to the coefficient on b1 when b2 is centered.

Improve this answer
$\endgroup$
5
  • $\begingroup$ Hi Noah! Thanks for your reply. So do you mean that the author might have just included an interaction term as a control variable rather than centering b2? Is this just a matter of preferences? $\endgroup$ Commented May 11, 2023 at 18:11
  • $\begingroup$ Everything I mentioned in my reply about centering b2 is in the context of including an interaction between b1 and b2. Centering a variable in the absence of an interaction doesn't change the slope values or interpretations. The author probably included an interaction because they thought the interaction model was closer to the correct model for the data or they wanted to investigate the interaction. Without the article I can only speculate. $\endgroup$ Commented May 11, 2023 at 18:15
  • $\begingroup$ If the authors did think that the interaction model was closer to the correct model, then that probably means they thought b1 when b2=0 is the most meaningful results of the model right? $\endgroup$ Commented May 11, 2023 at 20:12
  • $\begingroup$ Sorry Im new to econometrics so a lot of these questions might be nonsense.. $\endgroup$ Commented May 11, 2023 at 20:12
  • $\begingroup$ If they chose to test and interpret the coefficient b1, then yes, they thought b2=0 was meaningful. It's still not a very good summary when b2 is not properly centered. If b2 is categorical, then b2 = 0 is a meaningful value; it's the reference category, in which case the coefficient on b1 is the effect of b1 for the reference category. $\endgroup$ Commented May 11, 2023 at 20:25

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.