# BQ: Estimates a Blanchard-Quah type SVAR In cheaton/vars2: VAR Modelling

## Description

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

## Usage

 1 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{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:

 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().

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.

LÃ¼tkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

SVAR, VAR

## Examples

 1 2 3 data(Canada) var.2c <- VAR(Canada, p = 2, type = "const") BQ(var.2c) 

cheaton/vars2 documentation built on Oct. 1, 2018, 12:22 a.m.