vars (version 1.5-3)

# BQ: 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().

## 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().

## 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.

## 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.

L<U+34AE5C2F>hl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

SVAR, VAR

## Examples

Run this code
# NOT RUN {