HW2 (Due on Nov 10)
ECO 512; Time Series Econometrics
contains quarterly CD (91 days) rates from 1991.Q1 to 2013.Q4; GDP.txt
contains GDP growth rates (year-on-year) from 1971.Q1 to 2013.Q4; and
CPI.txt contains consumer price index from 1965.Q1 to 2013.Q4.
Now, consider a VAR(2) consisting of ination rates, GDP growth rates,
and CD interest rates. Ination rates are obtained as 100 (logCPIt
logCPIt4).
(a) Report the least squares estimates of VAR coe¢ cients and their
standard errors.
(b) Plot impulse response functions up to 16 horizons. In doing so,
identify structural parameters using short-run restrictions by assuming that
the causal chain holds in the order of ination rates, GDP growth rates and
CD interest rates. Interpret your results.
(c) Repeat (b) with long-run restrictions. How do your results change?
Explain main di¤erences.
2. Suppose that the data generating process is given by
yt = + ut (t = 1; : : : ; T )
ut = aut1 + et + bet1
et iid(0; 2e)
where ut is assumed to be a causal invertible process.
(a) Consider ^, the OLS estimate for . Suppose that the limiting
distribution of ^ is given by
p
T (^ ) d! N(0; s2).
1
Express s2 in terms of a, b and 2e.
(b) Consider the following estimate for 2 = V ar(ut)
^2 =
1
T
X
(yt ^)2 .
Derive the probability limit of ^2 in terms of a, b and 2e.
(c) Provide a condition on a and b under which it holds
p
T (^ )
^
d! N(0; 1).
2