BQ: Estimates a Blanchard-Quah type SVAR

In vars: VAR Modelling

Estimates a Blanchard-Quah type SVAR

Description

This function estimates a SVAR of type Blanchard and Quah. It returns a list object with class attribute ‘svarest’.

Usage

BQ(x)

Arguments

x	Object of class ‘varest’; generated by VAR().

Details

For a Blanchard-Quah model the matrix A is set to be an identity matrix with dimension K. The matrix of the long-run effects is assumed to be lower-triangular and is defined as:

(I_K - A_1 - \cdots - A_p)^{-1}B

Hence, the residual of the second equation cannot exert a long-run influence on the first variable and likewise the third residual cannot impact the first and second variable. The estimation of the Blanchard-Quah model is achieved by a Choleski decomposition of:

(I_K - \hat{A}_1 - \cdots - \hat{A}_p)^{-1}\hat{\Sigma}_u (I_K - \hat{A}_1' - \cdots - \hat{A}_p')^{-1}

The matrices \hat{A}_i for i = 1, \ldots, p assign the reduced form estimates. The long-run impact matrix is the lower-triangular Choleski decomposition of the above matrix and the contemporaneous impact matrix is equal to:

(I_K - A_1 - \cdots - A_p)Q

where Q assigns the lower-trinagular Choleski decomposition.

Value

A list of class ‘svarest’ with the following elements is returned:

A	An identity matrix.
Ase	NULL.
B	The estimated contemporaneous impact matrix.
Bse	NULL.
LRIM	The estimated long-run impact matrix.
Sigma.U	The variance-covariance matrix of the reduced form residuals times 100.
LR	NULL.
opt	NULL.
start	NULL.
type	Character: “Blanchard-Quah”.
var	The ‘varest’ object ‘x’.
call	The call to BQ().

Author(s)

Bernhard Pfaff

References

Blanchard, O. and D. Quah (1989), The Dynamic Effects of Aggregate Demand and Supply Disturbances, The American Economic Review, 79(4), 655-673.

Hamilton, J. (1994), Time Series Analysis, Princeton University Press, Princeton.

Lütkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

See Also

SVAR, VAR

Examples

data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
BQ(var.2c)

vars documentation built on March 31, 2023, 10:30 p.m.