Expectations: Suppose that at time time t5 the expected value of a random variable is 0:05: Moreover, you observe realizations of in subsequent periods till time t:

^t5 = 0:04; ^t4 = 0:03; ^t3 = 0:02; ^t2 = 0:01; ^t1 = 0:10:

(a) What is the expected value of at time t under adaptive expectations with = 1

(i.e., static expectations)?

(b) What is the expected value of at time t under adaptive expectations with = 13 ?

(c) What is the expected value of at time t under type 1 expectations? (Hint: Suppose t = 10)

(d) What is the expected value of at time t under rational expectations? Can you actually derive it? Why yes/no? Explain.