Estimates a Blanchard-Quah type SVAR
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 ‘ |
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.
A list of class ‘svarest’ with the following elements is
returned:
A |
An identity matrix. |
Ase |
|
B |
The estimated contemporaneous impact matrix. |
Bse |
|
LRIM |
The estimated long-run impact matrix. |
Sigma.U |
The variance-covariance matrix of the reduced form residuals times 100. |
LR |
|
opt |
|
start |
|
type |
Character: “Blanchard-Quah”. |
var |
The ‘ |
call |
The |
Bernhard Pfaff
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.
data(Canada) var.2c <- VAR(Canada, p = 2, type = "const") BQ(var.2c)
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