New Evidence on the Puzzles. Results from Agnostic Identification on Monetary Policy and Exchange Rates.

3 Our Approach

3.1 Methodology

Consider a vector autoregression in reduced form,

Yt = B(L)Yt-I + ut, E[utut] = Σ

for some vector of variables Yt, coefficient matrices B(L) and a variance-
covariance matrix for the one-step ahead prediction error Σ. The key to
identification is to represent the one-step ahead prediction error u_t as a linear
combination of orthogonalized “structural” shocks,

ut = Avt , E [utu^′_t] = I

Traditional identification strategies impose a recursive ordering or structural
restrictions on A or A^-1. Here, we use the methodology of sign restrictions
as in Uhlig (2005).

As a consequence, it is not necessary to identify all structural shocks.
Identifying a single shock is equivalent to identifying an impulse vector:

Definition 1 The vector a ∈ R^m is called an impulse vector, iff there is
some matrix A, so that AA = Σ and so that a is a column vector of A.

Simple matrix algebra shows that any impulse vector a can be character-
ized by

a = Aa,                             (5)

where AA' = Σ is some decomposition of Σ and a is an m-dimensional vector
of unit length. Let r_i(k) ∈ R^m be the vector response at horizon k to the i-th
shock in a Cholesky-decomposition of Σ. Then, the impulse response ra(k)
for a is given by

∞

ra(k) =     ai ri(k).                               (6)

i=1

11

<<   11   12   13   14   15   16   17   >>

More intriguing information