5. Functional Form and Interaction Terms Flashcards
Do explanatory variables have to be linear for OLS regression?
No it’s just the parameters that have to be linear
When are natural log transformations particularly useful?
When we want to measure relative changes because for small changes the change in the ln of a variable is roughly equal to the change in the variable
Double logs or log logs
Equations where both dependent and explanatory variables are logged
Level log
Where just the explanatory variables are logged
Log level
Where just the dependent variable is logged
How do we interpret B1 in a linear (level level) equation?
B1 is the change in y resulting from a unit change in x
How do we interpret B1 in a log log equation
Elasticity- B1 is the % change in y that results from a 1% change in x
How do we interpret B1 in a log level equation?
B1 x100 is the % change in y as a result of a unit change in x
How do we interpret B1 in a level log equation?
B1/100 is the change in y resulting in a 1% change in x
What variables can’t be logged?
Zero or negative values
What is the difference between a % change and a % point change?
- a %change is a change relative to the initial value
* a % point change is a change in a percentage
What do quadratic terms allow?
- marginal effects to change magnitude and sign
- models to accommodate non-linearity in relationship involving variables with observations that take zero or negative values
Why is comparing the quadratic model and a level log model problematic?
Because they are non nested and don’t contain the same variables
Which model do we prefer out of a quadratic model and a level log model?
- all other things equal we prefer the one that captured the non-linearity best
- we can use R^2 adapted to select the preferred model since they have the same dependent variable
When do interaction terms appear?
When the effect of x1 on y is dependent on x2 e.g. price elasticity depended on income
