Interaction term including year dummy while using year and industry fixed effects

[Jinwoong Lee]

Dear all,

I would like to ask a question about using an interaction term in a two-way fixed panel regression (year fixed effects and industry fixed effects).

Using a panel data from 2005 to 2020, I am trying to measure (1) if auditors charge more fees to the clients following a data breach and (2) if the level of response varies over time.

I came up with the following model, but I am not sure using the interaction variable (Breach*Year dummy) is a right choice.

Y = B0 + B1 * Breach + B2 * (Breach * Year dummy) + Controls + Year_FE + Industry_FE

where

• Y = Natural log of audit fees charged to a firm in year t
• Breach = 1 if a firm reported a data breach in year t, 0 otherwise
• Breach*Year dummy = Year-specific effect variable
• Controls = A group of control variables, such as firm size, profitability, etc.
• Year_FE = Year-fixed effect
• Industry_FE = Industry-fixed effect

In my understanding,

• B1(Breach) measures the effect of data breach on audit fees
• B2(Breach*Year dummy) measures if the effect of B1 changes over time or if any "year-specific" effect

Nonetheless, I cannot confirm if it is the right model for measuring the year-specific effect. I looked over Wooldridge (2016) but could not find a similar model.

Could anyone please comment on this model please? Any suggestion would be much appreciated.

[Jeff Wooldridge]

The coefficient on Breach is the effect in the first year and the coefficients on the interactions are the difference in the effect over each year compared with the first year.

[Jinwoong Lee]

Thank you so much for your comment, Dr. Wooldridge! I think that is what I need to test in this model. I really appreciate your help!!

[Jeff Wooldridge]

You’re welcome!