Let hy6t denote the three-month holding yield (in percent) from buying a six-month T-bill at time (t - 1) and selling it at time t (three months hence) as a three month T-bill. Let hy3t-1 be the three month holding yield from buying a three month T-bill at time (t - 1). At time (t - 1), hy3t-1 is known, whereas hy6t is unknown because p3t (the price of three-month T-bills) is unknown at time (t - 1). The expectations hypothesis (EH) says that these two different three-month investments should be the same, on average. Mathematically, we can write this as a conditional expectation:
E(hy6t/It-1) = hy3t-1,
where It-1 denotes all observable information up through time r - 1. This suggests estimating the model
hy61, = (0 + (1hy3t-1 + ut,
and testing H0: (1 = 1. (We can also test H0: (0 = 0, but we often allow for a term premium for buying assets with different maturities, so that (0 ( 0.)
(i) Estimating the previous equation by OLS using the data in INTQRT.RAW (spaced every three months) gives

(.070) (.039)
n = 123, R2 = .866.
Do you reject H0: (1 = 1 against H0: (1 ( t 1 at the 1% significance level? Does the estimate seem practically different from one?
(ii) Another implication of the EH is that no other variables dated as t - 1 or earlier should help explain hy6t, once hy3t-1 has been controlled for. Including one lag of the spread between six-month and three-month T-bill rates gives

(.067) (.039) (.109)
n = 123, R2 = .885.
Now, is the coefficient on hy3t-1 statistically different from one? Is the lagged spread term significant? According to this equation, if, at time t - 1, r6 is above r3, should you invest in six-month or three-month T-bills?
(iii) The sample correlation between hy3t and hy3t-1 is .914. Why might this raise some concerns with the previous analysis?
(iv) How would you test for seasonality in the equation estimated in part (ii)?

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hy6, 1)