How can I build a regression for this linear model?

Question

I have the following linear model, for which I want to build a regression.

[i,t] = [i]+[i][m,t] +[i][m,t][t]+[i,t]

r[i,t] and r[m,t] are the returns of financial data at time t and an equity index [i] or market[m], d[t] is a dummy variable which takes value 1 after a specific event and value 0 before the event. is an error term. the null hypothesis is H0: y[i] = 0; a rejection would mean H1a : y[i] < 0 or H1b: y[i] > 0

I'm not sure how to implement the y in my regression.

I would really appreciate your help. Thank you!

Answer 1

This is difficult to say without seeing your data, but looks like this could be expressed as a fixed effects model, where you have an interaction between R_{m,t} and D_{t}. However, there isn't really enough information to explain exactly how to implement this without more information about your model and data.

You can find an example of how this is implemented on this website (Econometrics with R) in general, with several approaches and functions (e.g. plm vesus lm, within versus first-difference).