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, S*B*D.
I am wondering if I absolutely have to include the two-way interaction variables:
S*B, B*D, 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!
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