i have a panel data set where the N dimension is countries(127 countries) and T dimension is year(2010 to 2015). I use a fixed effects to estimate a model of the form:

Y= b1X1+b2X2+b3X3+b4X4+u.

I estimate the model and i find that the coefficient b4 is negative. All variables are continuous.

I am interested now to check the hypothesis that the effect of X4 to Y changes over time (that is if the effect of X4 to Y changes as the time dimension T=years increases) and if the effect increases/decreases.

In order to check the hypothesis i re-estimate the model including an interaction term as:


I treat the variable years as continuous. My first question is if this approach is correct in order to test the hypothesis.

After i estimate the second model i find that the coefficient of the interaction term b6 is negative and significant and the main effect b4 is positive and significant. I know that the coefficient b4 in the second model is not comparable to the coefficient b4 in the first model.

My second question is how can i interpretate this results in terms of my hypothesis.

Thank you for your time My Best Regards.

  • $\begingroup$ In the first model was b4 statistically significant? In the second model which coefficients are statistically significant? The addition of year means the coefficients will change. Even if b4 is statistically in both models it could change signs because b4 no longer represents the full effect of X4 on Y. Some of it could be contained in the interaction term. $\endgroup$ Commented Mar 17, 2018 at 20:45
  • $\begingroup$ in the first model b4 was negative and significant.You are correct that in the second model the coefficients change. Does that mean that i can not use this approach to test my hypothesis?. If this is the case which approach could i use to test the hypothesis? My best Regards $\endgroup$
    – T. pachis
    Commented Mar 17, 2018 at 21:16

1 Answer 1


Yes, your approach is correct. The significance doesn't matter, your approach is correct regardless.

In your 2nd model, b4 is the effect of x4 when years = 0 (which it won't ever do unless you have centered years). b5 is the effect of years when X4 = 0 (it's not clear whether that ever happens).

One way to get a sense of the whole model is to set X1, X2 and X3 at their means and then graph predicted Y for various actual values of years and X4. You can also make a table of these values.

  • $\begingroup$ Thank you for your answer. I assume that your recommendation in order to get a sense of the whole model refers to the second model using the margins and marginsplot commands in stata for example. is that correct? $\endgroup$
    – T. pachis
    Commented Mar 17, 2018 at 23:15
  • $\begingroup$ I don't know Stata or what its commands do. $\endgroup$
    – Peter Flom
    Commented Mar 17, 2018 at 23:39

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