# Is difference-in-difference (did) an adequate model for this?

I am looking into whether fuel economy standards in the US (Wiki) have an influence on the footprint of a car (footprint is the area between the four wheels).

The fuel economy standard depends on the footprint of a car, the larger the footprint, the lower the fuel economy target (Be aware, that fuel economy is defined as miles/gallon which is different from liters/100 km which is the European way of describing the fuel efficiency of a car).

The fuel economy target is related to the footprint based on the curve shown in the picture below. A footprint <=41 or >= 56 have the same standard.

The obvious is that manufacturers would like to increase the footprint in order to comply with less stringent standards (miles/gallon) if their car is on the slope part of the curve. And they should have no incentive to increase the size of their car, if it is on the flat part of the curve.

Manufacturers redesign their cars about every four to five years and most of them change their footprint then.

I thought of a difference-in-difference model.

footprint ~ post.regulation + treatment.group + (post.regulation*treatment.group)

Base group contains all the vehicles that have a footprint larger than 56 or smaller than 41.

R-code:

did.lt = lm(footprint ~ treatment + postRegulation + did + origin,
data = exp.PvLtTwoMcFinal)
summary(did.lt)


Data I am looking at: Data One observation is per model cycle (or redesign) of a car which covers 4-5 years. The next observation is then for another model cycle.

Unfortunately, my model is not showing anything significant, which might be the fact, but...

(1) Am I doing something wrong here in terms of code and logic?

(2) My treatment group is larger (326 observations) than my base group (36 observations). Does it matter?

(3) My base group has a larger footprint on average than my base group. Does this matter?

(4) Are there other models that I could use in order to prove that vehicles sizes have increased?