# Can you interact the entity in fixed effects estimation?

I have estimated housing affordability (RRI) by fixed effects using the equation below:

The 'r' represents regional effects and 't' represents time effects.

This estimation works in Stata but are there any problems with including an interaction term which contains region? I couldn't find any information about this type of interaction. I get significant results so can I correctly conclude that there is an additional effect from the independent variables x1 and x2 from region one relative to the other regions.

I greatly appreciate any help. Thanks

• You need to explain how you are estimating the FEs. Are you just putting in dummies for region and time into an OLS specification, and maybe clustering the errors? How many regions and time periods do you have? – Dimitriy V. Masterov Apr 7 '15 at 23:05
• Thank you for your reply! I am estimating Fixed Effects using the xtreg, fe command on Stata (for the regional effects) and I am simply just putting in time dummies. I have 9 regions (the nine SSR regions of England) and 17 years of annual data (1996 - 2012). I am not clustering the errors. – Tom Markovitch Apr 7 '15 at 23:09
• In your equation you only have 2 regional dummies (assuming $r$ is region?) which would imply only 3 regions. IS your equation just a simplification and you actually have 8 dummy variables for 9 regions, or am I missing something? – robin.datadrivers Apr 8 '15 at 1:20
• Sorry, that is a typo. It should be both r1 only. This is because London behaves very differently than other regions in terms of a couple of the independent variables, for example in terms of housing stock and immigration. As x1, x2 and RRI are in logs, I believed the interpretation would be for example for lamdba1; a 1 percentage change increase in x1 would cause an additional percentage increase if the region is London, relative to all other regions. – Tom Markovitch Apr 8 '15 at 10:31

• @robin.datadrivers We might be getting into differences in terminology. Economists have a fairly unusual definition of FEs compared to other fields, and the first-difference or demeaning transformation will wipe out any time-invariant variables, even if they vary across panels. The xtreg, fe mentioned in the comments is consistent with the demeaning way of FE estimation. – Dimitriy V. Masterov Apr 8 '15 at 1:26