Interface for SVAR exclusion restrictions


y_t' A_0 = \sum_{i=1}^r y_{t-i} A_i + z_t' C + \epsilon_t

where yt 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 Ai, i=0,...,r.

The model can be written in a more compact form

y_t' A_0 = x_t A_+ + \epsilon_t


x_t = \left[\begin{array}{cccc}y_{t-1}' & \ldots & y_{t-r}' & z_t'\end{array}\right]\;\;\;
A_+ = \left[\begin{array}{c}A_1\\ \vdots \\ A_t\\ C\end{array}\right]

Exculsion Restrictions

Restrictions are defined with Qi and Ri matrices for each column of A0 and A+ respectively.

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

Q_i A_{0,i} = 0\;\;\;R_i A_{+,i} = 0

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

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

Dynare implementation

The Qi and Ri 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 yt,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 yt-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 and

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 =;
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);

ixmCoPres = NaN; }}}

and makes sure that the matrices have the right dimensions.

DynareWiki: SvarExclusionInterface (last edited 2011-11-06 14:59:48 by MichelJuillard)