Consider the following model:
Yt = B1 + B2Xt + B3Xt - 1 + B4Xt - 2 + B3Xt - 3 + ut
where Y = the consumption
X = the income
t = the time
This model states that consumption expenditure at time Ms a linear function of income not only at time t but also of income in three previous time periods. Such models are called distributed lag models and represent what are called dynamic models (i.e., models involving change over time).
a. Would you expect multicollinearity in such models and why?
b. If multicollinearity is suspected, how would you get rid of it?