What are the consequences of multicollinearity ? Consider the set of hypothetica

Question

What are the consequences of multicollinearity ?

Consider the set of hypothetical data in Table 10.10. Suppose you want to fit the model

Yi = 1 + 2X2i + 3X3i + ui

to the data.

a. Can you estimate the three unknowns? Why or why not?

b. If not, what linear functions of these parameters, the estimable functions, can you estimate? Show the necessary calculations.

Consider the following model:

Yt = 1 + 2Xt + 3Xt1 + 4Xt2 + 5Xt3 + 6Xt4 + ut

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.

a. Would you expect multicollinearity in such models and why?

b. If collinearity is expected, how would you resolve the problem?

In data involving economic time series such as GNP, money supply, prices, income, unemployment, etc., multicollinearity is usually suspected. Why?

Explanation / Answer

Answer for question 1)

Multicollinearity is the case in which independent variables in regression model are highly correlated .

When multicollinearity is present in given regression model then we can not use OLS methods to identify sample estimators

If we find the matrix of two independent variable vectors then matrix determinant is zero if multicollinearity is present in model which shows dependancy between independent variabkes. Another method of VIF can be used to identify multicollinearity.

To find value of sample estimate of population coefficient "b1" then b1 calculated from model using OLS method provides inflated values which are incorrect hence can't run hypothesis testing for such incorrect values of b1 and it's variance .

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