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svar1

structural VAR estimation

CALLING SEQUENCE

[A,B,param]=svar1(rvar,def_A,def_B,init)

PARAMETERS

Input

* rvar = rvar tlist returned by VAR

* def_A = a string matrix, defining its non-zero elements as constants or functions of the vector or parameters

   . 'A(i,j) = numerical value (e.g: 'A(1,1)=1')

   . 'A(i,j) = param(k)' (e.g: 'A(4,2)=param(3)')

* def_B = a string matrix, defining its non-zero elements as constants or functions of the vector of parameters

* init = a (nparam x 1) real vector, defining the satrting values of the vector of parameters (optional)

Output

* A = a (nvar x nvar) matrix, the estimated A matrix

* B = a (nvar x nvar) matrix, the estimated A matrix

* param = a (n x 1) vector, collecting the estimated parametrs of matrices A and B

DESCRIPTION

Switches from a VAR estimated in reduced form to a structural VAR, such as: B*u=A*eps with:

* u = (correlated) residuals from the reduced form

* eps = (uncorrelated) structural residuals.

EXAMPLE

// data are taken from Breitung J, Bruggemann R, and L¨utkepohl H (2004),
// Structural vector autoregressive modeling and  impulse responses,
// Applied Time Series Econometrics, Cambridge University Press

global GROCERDIR ;
load(GROCERDIR+'\data\breitung_et_al.dat')
var_breit=VAR(4,'endo=ly;lm;ir')
Def_A0=['A(2,1)=param(1)';'A(2,3)=param(2)';'A(3,1)=param(3)']

// A has the following form:
//     | 1			0		0  		 |
// A = | param(1) 	1		param(2) |
//     | param(3) 	0		1		 |

Def_B0=['B(1,1)=param(4)';'B(2,2)=param(5)';'B(3,3)=param(6)']

//     | param(4)	0		0  		 |
// B = | 0		 	param(5)		 |
//     | 0 	0		1		param(6) |

[A,B,param]=svar1(var_breit,Def_A0,Def_B0)

AUTHOR

Éric Dubois 2026

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