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

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

The matrices \hat{A}_i for i = 1, …, 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:

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)