Interaction term in fixed-effects model.

[Lander Seyma]

Dear all,

Let me ask you a question regarding interaction term.

I have an unbalanced panel data. I estimate the following regression by using fixed-effects model (i.e. I use 'xtreg..., fe robust' command in Stata):

flow(t) = alpha*volatility(t-1) + alpha(t-1) + volatility(t-1) + controls(t-1)

where the dep.variable is a percentage net flow, explanatory variables are interaction term, alpha (performance measure), perf.volatility, and other control variables.

So, the problem is that when I conduct this regression I receive insignificant coefficient on interaction term and significant estimates on other X's. However, when I remove 'alpha' from the model - I get highly significant estimates on interaction term, volatility and other controls!!!

As I know when one includes an interaction term between two ind.vars (x1 and x2), both these ind.variables must be included in the model as well. That's one cannot estimate regression with interaction term (x1*x2) having only x2 in the model. Is that true? Is it acceptable to remove one regressor from the regression having it only in the interaction term (i.e. you estimate y = x1*x2 + x2 + x3 + etc.).

All in all, I am confused. Can anybody, please, explain me - what's the problem with my regression and why do I get such insignificant coefficient on interaction term having all regressors included in the equation?

p.s. I have checked for multicollinearity, and it shows no evidence of multicollinearity (i.e. indep.vars' VIFs are below 10). I control for heteroscedasticity/autocorrelation by using 'robust' option.

I am grateful for any help on this issue.

[Richard Williams]

Just to be clear, are you estimating the model exactly as shown, or are you estimating

flow(t) = alpha(t-1)*volatility(t-1) + alpha(t-1) + volatility(t-1) + controls(t-1)

If not, then you aren't actually including both the main effects and the interaction term.

[Lander Seyma]

Hi Richard,

Yes, I estimate exactly this equation:
flow(t) = alpha*volatility + alpha + volatility + other control variables

explanatory var's are in time (t-1).

The problem is that the coefficient on the interaction term is absolutely insignificant!

[Richard Williams]

There is nothing that says an interaction term has to be significant so why does this concern you? Is such a finding counter to theory or inconsistent with previous research? If it is, then maybe you can take credit for proving that existing theories and research are wrong!

Getting back to your original post, it is generally a mistake to drop one of the main effects (in this case alpha) used to compute an interaction term. When you do this, the main effects and the interactive effects get confounded, i.e the interaction term alpha*volatility gets credit for what alpha alone was doing. You can think of it as a problem of omitted variable bias -- if an important variable gets left out, the estimated effects of remaining variables can be biased.

If you are convinced that there should be some sort of interaction, maybe you need to set it up differently, e.g. maybe volatility should be dichotomized rather than treated as continuous. Or maybe something should be logged or other transformations done.

[Lander Seyma]

I also read that one cannot just remove the explanatory variable that is included in interaction term. It is wrong. I am just wondering with the result I have once I remove alpha.
Yes, you are right - my result is inconsistent with prior research as past papers document a significant interaction term. That's why I am confused now.

Regarding interaction, I put it in the regression, because I want to examine the flow-performance sensitivity, i.e. how volatility affects this relationship.

Yes, I use volatility as a continuous variable. How would you recommend to dichotomize performance volatility?

[Richard Williams]

I don't know anything about the topic or past research, so I don't know why your results are different. Are you looking at different types of cases, different times, are you operationalizing things differently that other studies did, are your statistical methods or your models different? I think you'll just have to look at past research and see if there are any plausible reasons for the differences. You could make a big theoretical or empirical breakthough; or it could just be that others had better data than you did. Getting different results from past research can be good if you can make a good case for believing that your results are right and make sense (or can explain what everybody else did wrong). Getting different results may also mean that you need to rethink how you are doing things and see if there are any errors in your approach, your methods, or your data.

[Lander Seyma]

Richard, I am grateful for your advice.

I have read some notes on interaction terms and I would like to know - how to center continuous variable in Stata? I have seen some people recommend to center cont.variable before running a regression that includes the interaction term.

Can anybody explain me how to center a continuous variable at different levels in Stata?