# Interaction effects in Fixed Effect Models

#### MarkieMark

##### New Member
Dear all,

I am currently writing my Master thesis and in addition to finding a relationship, I examine whether the relationship between X and Y became stronger over time. I use a firm fixed effect model, and this is my base regression:

(1) CFO_TURNOVER = α0+α1INDUSTRY SHOCK+ ΣCONTROL VARIABLES +ε

I have 6 x variables and 6 control variables, the x variables are regressed separately. To examine whether the relationship became stronger, I created a new variable: year*x1 ,, year*x2 etc. (the interaction coefficient)

My question is, can I use year plain and simple use 2006,2007,2008 etc. as a variable., or do I need to create a categorical variable? Also, neither as a control or x-variable, year is included in my base regression. Since every interaction variable should also be in the regression individually, can I just add a variable year to my base regression?

With regards to the interpretation of the coefficient in a regression output, if it is significant, it indicates that the relationship is significantly different over time. A positive significant interaction coefficient would indicate that the effect became stronger over time and a significant negative effect would indicate that the relation became less strong?

Mark

#### MarkieMark

##### New Member
I figured it out and used a categorical variable for year: 2007 = 1, 2008 =2 etc. Base model (1), turns to this:

(2) CFO_TURNOVER = α0+αSHOCKS+ α2YEAR+ α3 YEAR*SHOCKS + ΣCONTROLS +ε

- Shocks stands for the 6 x-variables that are seperately regressed in the Fixed Effect Model.

The year variable is significant and negative: indicating that the relation between X and Y defers in the years. Does the sign of the year variable tell me extra information?
The interaction effect is significant and negative: indicating that the relation between X and Y is stronger in the beginnning of the sample period (i.e. higher categorical year variable decreases the effect of X on Y)

My real question here is: some of the X-variables in my base regression suddenly became significant in the regression with the year and interaction variables added. How is this possible and what does this tell me?

Kind regards,

Mark