S10 - Polynomials and Interactions

Question 1

Under which circumstances would we want to interact two variables in a regression model?

(Multiple answers possible)

Select one or more:

a. When we suspect that the effect of a certain variable on the dependent variables is conditioned by the value of a third variable

b. When we conclude multicollinearity is present after performing a VIF test. Interacting the two collinear independent variables will alleviate the problem.

c. When our theory stipulates that that our main independent variable of interest only has an effect on the dependent variable for certain categories of another variable

d. When we suspect that we have omitted variable bias.

Answer 1

Correct: A & C

We should include interaction terms when we suspect or when theory dictates that the effect of one variable on the dependent variable depends on the value of a third variable or on a given category of a third variable. Interactions will not alleviate multicollinearity and will not control for variables that you have not included in your model.

Question 2

Is the following statement true or false?
Models that calculate interaction terms should include at least two independent variables plus the interaction term.

True or false?

Answer 2

True. Every time you include an interaction, you should include the constitutive terms of the interaction in addition to the interaction! This will give at least two independent variables plus the interaction term.

Question 3

What is the correct interpretation of the coefficient for log_price?

a.
All other factors constant, a one percent increase in the price of cigarette packs leads to a 1.33 percent decrease in the consumption of cigarette packs, on average.

b.
All other factors constant, a dollar increase in the price of cigarette packs leads to a 1.33 percent decrease in the consumption of cigarette packs, on average.

c.
All other factors constant, one unit increase in the price of cigarette packs leads to a 1.33*100 percent decrease in the consumption of cigarette packs, on average.

d.
All other factors constant, one unit increase in the price of cigarette packs leads to a 1.33 unit decrease in the consumption of cigarette packs, on average.

Answer 3

Correct: A

Notice that we have a log-log regression. Therefore, as we have seen in the lecture, the correct interpretation is: All other factors constant, a one percent increase in the price of cigarette packs leads to a 1.33% percent decrease in the consumption of cigarette packs, on average.

Question 4

What is another common specification error?

Answer 4

Common specification error: falsely assuming that X’s effect on Y is unchanging/ has an constant effect

• the effect of X and Y may depend on a third variable, Z (interaction)
• The effect of X and Y may be different at different levels of X (non-linearity)

Question 5

Formulate the general H1 for a Dummy Interaction

Answer 5

H1: An increase in X is associated with an increase in Y when condition Z is met, but not when it is absent.

Question 6

when do we need an interaction term?

Answer 6

When the relationship between two variables depends on the level of a third variable, we need to interact them.

Question 7

Interval-Level Interaction // Continuous Interaction

Formulate the H1

Answer 7

The magnitude of the association between an increase in X and an increase in Y increases (decreases) as the magnitude of variable Z increases.

• build partial derivative
• marginal effects plot

If the interaction (aka “conditioning”, “moderating”) variable is interval level, it can take on multiple values and we’ll get one slope for every value of the interaction variable.

Interpretation: If all the variables are interval, the conditional effect of each x on y is just the “marginal” effect, ie. the first partial derivative.

(-> Merkregel bei partial derivatives: im Nenner steht, was in der Ableitung dann fallen gelassen wird.)