Consider the following model: Y t = 1 + 2 X t + 3 X t 1 + 4 X t

Consider the following model:

Y_t = β₁ + β₂X_t + β₃X_t−1 + β₄X_t−2 + β₅X_t−3 + β₆X_t−4 + u_t

where Y = consumption, X = income, and t = time. The preceding model postulates that consumption expenditure at time t is a function not only of income at time t but also of income through previous periods. Thus, consumption expenditure in the first quarter of 2000 is a function of income in that quarter and the four quarters of 1999. Such models are called distributed lag models, and we shall discuss them in a later chapter.
a. Would you expect multicollinearity in such models and why?
b. If collinearity is expected, how would you resolve the problem?