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I have a panel data set where Canadian provinces are the individuals. (I have annual data from 1997-2017).

I am using a random effects model to see the impact of an explanatory variable $X_{it}$ on a dependent variable $Y_{it}$ (as well as many controls) at a national level.

I'm also interested in just seeing the relationship for one province $j$. i.e. What effect did $X$ have on $Y$ only in province $j$ Is there any way to use my panel data to answer this question? Could I create a dummy for province $j$ and then interact it with $X_{it}$?

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  • $\begingroup$ Can you clarify how $𝑋_{𝑖𝑡}$ changes over time for each province and across provinces? $\endgroup$
    – dimitriy
    May 17, 2019 at 2:43
  • $\begingroup$ $X_{it}$ is the capital-to-labour ratio within the healthcare sector in each province in each year. So it is a continuous variable that differs somewhat (but not hugely) between provinces and either trends gradually up or down over time within each province. $\endgroup$ May 17, 2019 at 13:01

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You want to run your model with $X_{it}$, a dummy for province $j$, and the interaction of the dummy and $X_{it}$ on the right-hand-side. The coefficient on the interaction will tell you if $X$ has an unusual effect in that province (relative to the others).

You might also want to interact your other covariates with the province $j$ dummy.

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  • $\begingroup$ Ok, thank you! Do you mean RHS (instead of LHS)? $\endgroup$ May 17, 2019 at 18:08
  • $\begingroup$ @leecarvallo Yes, I mean the other left. Let me fix. $\endgroup$
    – dimitriy
    May 17, 2019 at 18:53
  • $\begingroup$ Hi again Dimitriy, why should I interact my other covariates (my controls) with the province $j$ dummy as well? $\endgroup$ May 27, 2019 at 19:43
  • $\begingroup$ @leecarvallo Obviously, context matters and you should not put in interactions willy nilly, but use domain expertise. However, if you are worried that $X$ has a different effect in province $j$, that concern may apply to other covariates. $\endgroup$
    – dimitriy
    May 28, 2019 at 17:48
  • $\begingroup$ I see, thank you. So I should add interactions where conceptually there may be different effects between provinces? $\endgroup$ May 28, 2019 at 20:10

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