Suppose you want to model a set of interaction relationships among gun ownership, conservatism, and Republican ratings. You think that the positive effect of gun ownership on Republican ratings is significantly stronger for conservatives than nonconservatives. To construct the interaction model, you will build on the base effects of the model shown in Exercise 5: y = a b1 (owner) b2 (conservative), where “owner” is the gun owner/ nonowner dummy and “conservative” is the conservative/ nonconservative dummy. Before you specify the model, you will need to compute an interaction variable.
A) (i) The interaction variable is computed by multiplying ______________ times ______________. (ii) Which one of the following groups of respondents will have a value of 1 on the interaction variable: gun-owning nonconservatives, nongun-owning nonconservatives, gun-owning conservatives, nongun-owning conservatives?
B) Write out the interaction model to be estimated.
C) Focus on the coefficient that estimates the interaction effect. (i) If your idea is correct— that the positive effect of gun ownership on Republican ratings is significantly stronger for conservatives than for nonconservatives— then would you expect the sign on the coefficient to be negative, positive, or close to 0? (ii) Explain your answer.