Stata - cross-sectional panel regression

#1
Hello,

I want to predict returns of real estate investment trusts (REITs) in excess of the risk-free rate (rf), by using various explanatory variables which are market risk premium, the Fama&French factors and the Carhart momentum factor (MOM). For those not familiar with them; the market risk premium is the return on the market in excess of the risk free rate (MKT-RF), the Fama&French factors are size (SMB) and book-to-market ratio (HML), which basically say that being small enhances returns, and having a high book-to-market ratio contributes positively to returns as well. The momentum factor says that firms who did well in the past year, continue to do so next period. In addition, I have a leverage factor. So far, so good. However, how do I perform a regression on this dataset? Since I have multiple REITs I’ve set my data as panel data, and usually I would just do: reg y x1 x2 x3 x4 and so on. But how can I incorporate Country effects in this regression? It is sufficient to do: xtreg y x1 x2 x3 x4 i.Country?

To make things more complicated REITs can operate in only one Sector. But I expect returns to vary amongst Sectors as well, can I in that case do: xtreg y x1 x2 x3 x4 i.Country i.Sector? Or does this accounts for the effect of a certain sector in a country (the combined effect) or for the separate effect of countries and sectors? As you might guess from my type of questions, I’m not really a professional when it comes to statistics…

Furthermore, how would I formally formulate this test? My current formulation is in the attachment. Note that the subscripts i are for the individual REIT effect, since all those factors differ per REIT. The subscript t denotes the date.

I would be very glad if you could give me a hint in the right direction,
Thanks in advance!
 
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