• SvarExclusionInterface

Interface for SVAR exclusion restrictions

Model

where y_t is a vector of n endogenous variables, r is the maximum lag length, z a vector of m exogenous variables (only a constant for the time being).

Note that each equation corresponds to the columns of A_i, i=0,...,r.

The model can be written in a more compact form

where

Exculsion Restrictions

Restrictions are defined with Q_i and R_i matrices for each column of A₀ and A₊ respectively.

Q and R matrices are made of 0 and 1 such that

Q_i matrices have n columns and as many rows as there are restrictions.

R_i matrices have k=r*n+1 columns and as many rows as there are restrictions.

Dynare implementation

The Q_i and R_i matrices are stored in 2 cell arrays, with as many elements as equations:

Qi = cell(n);
Ri = cell(n);

Each element of the cell arrays is a matrix with as many rows as there are restrictions on the equation and as many columns as there are coefficients in A₀ and A₊ respectively.

For each exclusion of variable y_t,j in equation i

Qi{i}(h,j) = 1;

where h is the number of the restriction in equation i in A₀

For each exclusion of variable y_t-p,j in equation i

Ri{i}(h,(p-1)*n+j) = 1;

where h is the number of the restriction in equation i in A₊

For general linear restrictions on the coefficients, the non-zero elements of the matrices in Qi and Ri are not necessarily equal to 1.

Excluding the constant in equation i requires setting

Ri{i}(h,r*n+1) = 1;

The preprocessor creates options_.ms.Qi and options_.ms.Ri

The Matlab function swz/identification/exclusions.m handles these options, except when upper_cholesky or lower_cholesky are specified. It contains the following code:

%make local copy in order not to call structure fields inside a loop
Qi = options_.ms.Qi;
Ri = options_.ms.Ri;
for n=1:nvar
 Ui{n" = null(Qi(:,:,n));
 Vi{n} = null(Ri(:,:,n));
 n0(n) = size(Ui{n},2);
 np(n) = size(Vi{n},2);
end

ixmCoPres = NaN; }}}

and makes sure that the matrices have the right dimensions.