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

’.

`BQ(x)`

x

Object of class ‘`varest`

’; generated by
`VAR()`

.

A list of class ‘`svarest`

’ with the following elements is
returned:

An identity matrix.

`NULL`

.

The estimated contemporaneous impact matrix.

`NULL`

.

The estimated long-run impact matrix.

The variance-covariance matrix of the reduced form residuals times 100.

`NULL`

.

`NULL`

.

`NULL`

.

Character: “Blanchard-Quah”.

The ‘`varest`

’ object ‘`x`

’.

The `call`

to `BQ()`

.

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.

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.

```
# NOT RUN {
data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
BQ(var.2c)
# }
```

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