vars (version 1.1-9)

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().

encoding

latin1

concept

• SVAR
• Structural VAR
• Structural Vector Autoregressive
• Blanchard-Quah

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�tkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

See Also

SVAR, SVAR2, VAR

Examples

data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
BQ(var.2c)