Say I have a set of time series data spanning 2000-2016
I code my years as the variable time, starting in 2000 as 0, 1, 2,....15
Say I want to compare the bush presidency to the obama presidency and so code the bush variable as 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0.... and then the obama as 0, 0, ... 0, 1, 2, 3, 4, 5, 6, 7.
Would I expect multi-collinearity between these time variables? They are linear combinations.
Is it necessary to have the variable time when bush+obama=time
To more accurately model
GDP = bush+obama+time
GDP = bush+obama
where the goal is to find the annual change in GDP (as opposed to the mean change).
my thoughts are -
time accounts for the overall serial correlation
the coefficients for bush and obama provide their effect on GDP with the serial correlation controlled for.