2
$\begingroup$

I am testing the effect of commodity demand shocks to the foreign exchange market. Because my hypotheses include three-way interaction effects, I test my hypotheses using hierarchical regression model. Is it absolutely necessary to include all lower-level interactions?

Assume that the 3 variables are the following: shocks in commodity demand (say variable S), country commodity balance of trade (B) and a dummy variables =1 if the country is a commodity net exporter, =0 if the country is a commodity net importer (say variable D)

In my model, I include three-way interaction variables in model 3, SBD.

I am wondering if I absolutely have to include the two-way interaction variables: SB, BD, and D*S as well as S, D and B as stand alone independent variables.

Please let me know what you think and why it makes sense in economic and econometric terms. Thanks a lot in advance!

Improve this question
$\endgroup$
0

1 Answer 1

Reset to default
1
$\begingroup$

Do you have to? Of course not, free country, what? If you don't, then you make some assertions that you may not wish to make. Take a model with only the three-way interaction: $$Y=\beta_0+\beta_7 SBD+e$$ Now look at the simple slope of, say, S, by taking the derivative of Y with respect to S, and you get: simple slope of S = $\beta_7 BD$ OK? Well, sure, but what if either B or D = 0? Then the simple slope of S is also 0. Maybe you don't have 0 values for B or D (or S) in your data...but are you comfortable with this assertion about the S-Y relationship (which, in slightly different form, you will be making about the B-Y and D-Y relationships)? In leaving out lower level interactions, you also backhandedly make assertions about other terms having no relation to the dependent variable. And you might even be right...but those will be untested assumptions looming over your conclusions.

Improve this answer
$\endgroup$
2
  • $\begingroup$ Thanks a lot for your response Ed. Is there any way to test the assumption that I am making by leaving out the level variables? What would be the correct econometric test that would allow me to justify my choice. Thanks in advance. $\endgroup$ Commented Mar 14, 2020 at 6:09
  • $\begingroup$ Sorry to take so long to reply. I would start by graphing the data in this range, where the variables take on 0 values. If the variables do not take on 0 values in your dataset, then any conclusion amounts to extrapolation and is of limited value. Of course, you can conduct nested F tests (with and without the terms in question). A failure to reject the null that the terms contribute nothing to prediction is suggestive, but... $\endgroup$ Commented Mar 18, 2020 at 16:56

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.