Consider a model with dependent variable Y and independent variable X, and data over a 120 quarter time-span.
a) Write out a regression with quarter dummies (use summation notation to be compact). How is this same as a time fixed effects regression?
b) Write out a regression equation with a variable “time,” which takes on the value 1 at the beginning of the sample and 120 at the end of the sample.
c) How are the regressions in (a) and (b) different? Which one will fit the data better and why?