This function estimates a SVAR of type Blanchard and Quah. It returns
a list object with class attribute ‘svarest’.
BQ(x)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().
Object of class ‘varest’; generated by
VAR().
Bernhard Pfaff
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.
Lütkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.
SVAR, VAR
data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
BQ(var.2c)
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