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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.

Target cure

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?

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First speaking to the economics of the problem, there is still an incentive to increase the footprint of cars below the slope.

Regarding the diff-in-diff, what is your treatment? The implementation of this regulation in 2012?

This seems like a regression kink design would be better, given the discrete change in incentives at the end of the slope. Or a variable-intensity diff-in-diff, since cars closer to the upper cutoff are not going to be affected as much.

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  • $\begingroup$ Vehicles larger than 56 ft^2 should have no incentive to increase the size in order to better comply with the standard. The increase does not lower the fuel economy but punishes this particular vehicle as the weight increases and therefore negatively affects the fuel economy. The treatment group are the vehicles that are on the flat parts of the curve as their fuel economy target does not change when size is increased. The year is 2011 when die Regulation was effective. $\endgroup$ – Bert Sep 25 '16 at 0:20
  • $\begingroup$ The treatment group are the vehicles that are on the flat parts of the curve as their fuel economy target does not change when size is increased. The year is 2011 when die Regulation was effective. $\endgroup$ – Bert Sep 25 '16 at 0:26
  • $\begingroup$ Do you mind elaboration a bit on the regression kink design as this concept is new to me. With variable-intensity diff-in-diff you mean assigning weights? Do you have an example for that? $\endgroup$ – Bert Sep 25 '16 at 0:26

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