FAVAR | R Documentation |
Estimate a FAVAR model by Bernanke et al. (2005).
FAVAR( Y, X, fctmethod = "BBE", slowcode, K = 2, plag = 2, factorprior = list(b0 = 0, vb0 = NULL, c0 = 0.01, d0 = 0.01), varprior = list(b0 = 0, vb0 = 0, nu0 = 0, s0 = 0, mn = list(kappa0 = NULL, kappa1 = NULL)), nburn = 5000, nrep = 15000, standardize = TRUE, ncores = 1 )
Y |
a matrix. Observable economic variables assumed to drive the dynamics of the economy. |
X |
a matrix. A large macro data set. The meanings of |
fctmethod |
|
slowcode |
a logical vector that identifies which columns of X are slow
moving. Only when |
K |
the number of factors extracted from |
plag |
the lag order in the VAR equation. |
factorprior |
A list whose elements is named sets the prior for the factor equation.
|
varprior |
A list whose elements is named sets the prior of VAR equations.
|
nburn |
the number of the first random draws discarded in MCMC. |
nrep |
the number of the saved draws in MCMC. |
standardize |
Whether standardize? We suggest it does, because in the function VAR equation and factor equation both don't include intercept. |
ncores |
the number of CPU cores in parallel computations. |
Here we simply state the prior distribution setting of VAR. VAR could be written by (Koop and Korobilis, 2010),
y_t= Z_tβ + \varepsilon_t, \varepsilon_t\sim N(0,Σ)
You can write down it according to data matrix,
Y= Zβ + \varepsilon, \varepsilon\sim N(0,I\otimes Σ)
where Y = (y_1,y_2,\cdots, y_T)',Z=(Z_,Z_2,\cdots,Z_T)',\varepsilon=(\varepsilon_1,\varepsilon_2,\cdots,\varepsilon_T). We assume that prior distribution of β and Σ^{-1} is,
β\sim N(b0,V_{b0}), Σ^{-1}\sim W(S_0^{-1},ν_0)
Or you can set the Minnesota prior for variance of β, for example, for the mth equation in y_t= Z_tβ + \varepsilon_t,
\frac{κ_0}{l^2},l is lag order, for won lags of endogenous variables
\frac{κ_0κ_1}{l^2}\frac{σ_m^2}{σ_n^2}, m\ne n,for lags of other endogenous variables in the mth equation, where σ_m is the standard error for residuals of the mth equation.
Based on the priors, you could get corresponding post distribution for the parameters by Markov Chain Monte Carlo (MCMC) algorithm. More details, see Koop and Korobilis (2010).
An object of class "favar" containing the following components:
A list. The estimation results of VAR including estimated coefficients
A
, their variance-covariance matrix sigma
, and other statistical summary for A
.
A array with 3 dimension. and Lamb[i,,]
is factor loading matrix
for factor equations in the ith sample of MCMC.
Extracted factors from X
.
Model information containing nburn,nrep,X,Y
and p
, the number of endogenous variables
in the VAR.
Bernanke, B.S., J. Boivin and P. Eliasz, Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach. Quarterly Journal of Economics, 2005. 120(1): p. 387-422.
Boivin, J., M.P. Giannoni and I. Mihov, Sticky Prices and Monetary Policy: Evidence from Disaggregated US Data. American Economic Review, 2009. 99(1): p. 350-384.
Koop, G. and D. Korobilis, Bayesian Multivariate Time Series Methods for Empirical Macroeconomics. 2010: Now Publishers.
summary.favar
, coef.favar
and irf
. All of them are
S3 methods of the "favar" object, and
summary.favar
that prints the estimation results of a FAVAR model, and
coef.favar
that extracts the coefficients in a FAVAR model, and
irf
that computes the impulse response in a FAVAR model.
# data('regdata') # fit <- FAVAR(Y = regdata[,c("Inflation","Unemployment","Fed_funds")], # X = regdata[,1:115], slowcode = slowcode,fctmethod = 'BBE', # factorprior = list(b0 = 0, vb0 = NULL, c0 = 0.01, d0 = 0.01), # varprior = list(b0 = 0,vb0 = 10, nu0 = 0, s0 = 0), # nrep = 15000, nburn = 5000, K = 2, plag = 2) ##---- print FAVAR estimation results------ # summary(fit,xvar = c(3,5)) ##---- or extract coefficients------ # coef(fit) ##---- plot impulse response figure------ # library(patchwork) # dt_irf <- irf(fit,resvar = c(2,9,10))
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