R: Estimates a Blanchard-Quah type SVAR

BQ {vars} | R Documentation

## 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{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()`.

### 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)

[Package vars version 1.5-3 Index]