(a) Suppose that a researcher has a set of three variables, yt

(t =

1, …, T), i.e., yt denotes a p-variate, or p × 1 vector, that she wishes to test for the existence of cointegrating relationships using the Johansen procedure.

What is the implication of finding that the rank of the appropriate matrix takes on a value of

(i) 0 (ii) 1 (iii) 2 (iv) 3?

(b) The researcher obtains results for the Johansen test using the variables outlined in part

(a) of the question as follows r λmax 5%

critical value 0 38.65 30.26 1 26.91 23.84 2 10.67 17.72 3 8.55 10.71 Determine the number of cointegrating vectors, explaining your answer.