FAVAR {FAVAR}

FAVAR

Description

Estimate a FAVAR model by Bernanke et al. (2005).

Usage

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
)

Arguments

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 X and Y is same as ones of Bernanke et al. (2005).

fctmethod

'BBE' or 'BGM'. 'BBE'(default) means the factors extracted method by Bernanke et al. (2005), and 'BGM' means the factors extracted method by Boivin et al. (2009).

slowcode

a logical vector that identifies which columns of X are slow moving. Only when fctmethod is set as 'BBE', slowcode is valid.

K

the number of factors extracted from X.

plag

the lag order in the VAR equation.

factorprior

A list whose elements is named sets the prior for the factor equation. b0 is the prior of mean of regression coefficients \beta,and vb0 is the prior of the variance of \beta, and c0/2 and d0/2 are prior parameters of the variance of the error \sigma^{-2}, and they are the shape and scale parameters of Gamma distribution, respectively.

varprior

A list whose elements is named sets the prior of VAR equations. b0 is the prior of mean of VAR coefficients \beta, and vb0 is the prior of the variance of \beta, it's a scalar that means priors of variance is same, or a vector whose length equals the length of \beta. nu0 is the degree of freedom of Wishart distribution for \Sigma^{-1}, i.e., a shape parameter, and s0 is a inverse scale parameter for the Wishart distribution, and it's a matrix with ncol(s0)=nrow(s0)=the number of endogenous variables in VAR. If it's a scalar, it means the entry of the matrix is same. mn sets the Minnesota prior. If varprior$mn$kappa0 is not NULL, b0,vb0 is neglected. mn's element kappa0 controls the tightness of the prior variance for self-variables lag coefficients, the prior variance is \kappa_0/lag^2, another element kappa1 controls the cross-variables lag coefficients spread, the prior variance is \frac{\kappa_0\kappa_1}{lag^2}\frac{\sigma_m^2}{\sigma_n^2}, m\ne n. See details.

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.

Details

Here we simply state the prior distribution setting of VAR. VAR could be written by (Koop and Korobilis, 2010),

y_t= Z_t\beta + \varepsilon_t, \varepsilon_t\sim N(0,\Sigma)

You can write down it according to data matrix,

Y= Z\beta + \varepsilon, \varepsilon\sim N(0,I\otimes \Sigma)

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 \beta and \Sigma^{-1} is,

\beta\sim N(b0,V_{b0}), \Sigma^{-1}\sim W(S_0^{-1},\nu_0)

Or you can set the Minnesota prior for variance of \beta, for example, for the mth equation in y_t= Z_t\beta + \varepsilon_t,

• \frac{\kappa_0}{l^2},l is lag order, for won lags of endogenous variables

• \frac{\kappa_0\kappa_1}{l^2}\frac{\sigma_m^2}{\sigma_n^2}, m\ne n,for lags of other endogenous variables in the mth equation, where \sigma_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).

Value

An object of class "favar" containing the following components:

varrlt

A list. The estimation results of VAR including estimated coefficients A, their variance-covariance matrix sigma, and other statistical summary for A.

Lamb

A array with 3 dimension. and Lamb[i,,] is factor loading matrix for factor equations in the ith sample of MCMC.

factorx

Extracted factors from X

.

model_info

Model information containing nburn,nrep,X,Y and p, the number of endogenous variables in the VAR.

References

1. 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.

2. 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.

3. Koop, G. and D. Korobilis, Bayesian Multivariate Time Series Methods for Empirical Macroeconomics. 2010: Now Publishers.

See Also

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.

Examples

# 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))