estimate_bsvar {bsvars} | R Documentation |

Estimates the homoskedastic SVAR using the Gibbs sampler proposed by Waggoner & Zha (2003)
for the structural matrix `B`

and the equation-by-equation sampler by Chan, Koop, & Yu (2021)
for the autoregressive slope parameters `A`

. Additionally, the parameter matrices `A`

and `B`

follow a Minnesota prior and generalised-normal prior distributions respectively with the matrix-specific
overall shrinkage parameters estimated using a 3-level hierarchical prior distribution.
See section **Details** for the model equations.

```
estimate_bsvar(S, specification, thin = 10, show_progress = TRUE)
```

`S` |
a positive integer, the number of posterior draws to be generated |

`specification` |
an object of class BSVAR generated using the |

`thin` |
a positive integer, specifying the frequency of MCMC output thinning |

`show_progress` |
a logical value, if |

The homoskedastic SVAR model is given by the reduced form equation:

`Y = AX + E`

where `Y`

is an `NxT`

matrix of dependent variables, `X`

is a `KxT`

matrix of explanatory variables,
`E`

is an `NxT`

matrix of reduced form error terms, and `A`

is an `NxK`

matrix of autoregressive slope coefficients and parameters on deterministic terms in `X`

.

The structural equation is given by

`BE = U`

where `U`

is an `NxT`

matrix of structural form error terms, and
`B`

is an `NxN`

matrix of contemporaneous relationships.

Finally, the structural shocks, `U`

, are temporally and contemporaneously independent and jointly normally distributed with zero mean and unit variances.

An object of class PosteriorBSVAR containing the Bayesian estimation output and containing two elements:

`posterior`

a list with a collection of `S`

draws from the posterior distribution generated via Gibbs sampler containing:

- A
an

`NxKxS`

array with the posterior draws for matrix`A`

- B
an

`NxNxS`

array with the posterior draws for matrix`B`

- hyper
a

`5xS`

matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution

`last_draw`

an object of class BSVAR with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using `bsvar()`

.

Tomasz Woźniak wozniak.tom@pm.me

Sampling from the generalised-normal full conditional posterior distribution of matrix `B`

is implemented using the Gibbs sampler by:

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. *Journal of Economic Dynamics and Control*, **28**, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Sampling from the multivariate normal full conditional posterior distribution of each of the `A`

matrix row is implemented using the sampler by:

Chan, J.C.C., Koop, G, and Yu, X. (2021) Large Order-Invariant Bayesian VARs with Stochastic Volatility.

`specify_bsvar`

, `specify_posterior_bsvar`

, `normalise_posterior`

```
# upload data
data(us_fiscal_lsuw)
# specify the model and set seed
specification = specify_bsvar$new(us_fiscal_lsuw, p = 4)
set.seed(123)
# run the burn-in
burn_in = estimate_bsvar(50, specification)
# estimate the model
posterior = estimate_bsvar(100, burn_in$get_last_draw())
```

[Package *bsvars* version 1.0.0 Index]