Interpreting the interaction effect in a well known paper

Attached you will find a well known research paper. If you go to page 438 (page 9 of the pdf file) you will find a model where:

change in tax rate = b1xMiss + b2x Miss Amount +b3(Miss x Miss Amount) + controls

according to the model , firms play with their accounts in order to pay less taxes when they miss the earnings per share of analysts' forecast.
So miss is a dummy that takes the value of 1 if firms miss analysts forecasts and zero otherwise.
Miss amount is by how much the firms miss the earnings per share of analysts (in other words it is EPS of analysts - realized EPS by the firm) and Miss x Miss Amount is the interaction term.

The issue , although it is explained briefly in the paper, I can't interpret b0,b1,and b2 due to the fact that miss takes the value of 1 if miss amount is positive . So why to interact something on itself. the journal is a top journal , so i must be missing something. Can someone help me to interpret the 3 coefficients (b1,b2, and b3) since i found them very confusing.


TS Contributor
I think you are right, and the problem is that Miss and MissAmount are not independent: you can only have a nonzero MissAmount if Miss is 1 (unless they define MissAmount in a way that it can be negative if they are above target, I didnt check that).

If MissAmount is non-zero only if they actually miss the target, then this is simply a fancy way of expressing the model




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It's possible for MissAmount to be negative right? This is just allowing the model to have a different slope/intercept for MissAmount for when it is negative and when it is positive.


TS Contributor
I couldn't really figure out from the text, whether MissAmount can be negative or not - if it can then of course the original model makes sense.

yes miss amount could be either negative or positive because the firm can exceed analyst forecasts(negative miss amount) or it can fall short of analysts forecasts (in this case miss amount is positive). Only in the latter case the firm has an incentive to manipulate its accounts to decrease its tax payment
I used a similar model in a different context but the results are difficult to interpret. for example :
miss coefficient (i.e b1)=.0047225 with a p value of 0.08 |
missamount coefficient (i.e b2)= .023954 with p value=0.01
miss x missamount coefficient (i.e b3) = -.0188994 with p value= 0.001

Q1: How can miss and missxmissamount have different signs?
Q2: also how can missamount and miss x missamount lead both to an increase in the dependent variable (I assume when we interact then the 2nd term (miss amount) will be for the firms with negative miss amount) and the miss amount in the interaction term is for firms with positive miss amount)
Q3:when interpreting the results should i add b1 to b3 when discussing the effect on the dependent variable?

Happy new year. Getting a clear idea about these 3 questions will be a good start for the year :)