Incorporating COVID related Volatility in Semi-structural models

Estimation ML/Bayesian estimation
1

Dear all,

I am trying to estimate Laubach & Wiliams(2003) type model and incorporate Covid-related large volatility in the model.

Holston, Laubach and Williams(2023) introduced time-varying volatility by multiplying a scale factor \kappa_{t} to the shock variances of the model’s measurement equations. In their specification, \kappa_{t} is greater than 1 during the pandemic years(2020~2022) and the innovation variance increases.

When introducing the scale factor in my dynare code, the posterior estimates for KAPPA and covid related parameters seems not to reflect the information of data.
(i.e. posterior distribution is almost the same as prior distribution I considered, regardless of the type of distribution(e.g. normal, beta, inverse gamma,…))

I made \kappa_{t} be the linear sum of year dummies d_2020, d_2021, d_2022 as follows :

KAPPA = ( 1+ k2020d_2020 + k_2021d_2021 + k_2022*d_2022 )

How can I deal with this kind of time-varying volatility using dynare?

If detailed sample code script is needed, please see the attached files.

LW_covid.mod (5.7 KB)
LW_covid_data.mat (7.2 KB)
main_LW_covid.m (684 Bytes)

2

Do I understand it correctly that you want to simply scale up the variance by a known and determinstic \kappa_t? In that case, you should use the heteroskedastic_filter-option. See e.g. tests/estimation/heteroskedastic_shocks/fs2000_het.mod · master · Dynare / dynare · GitLab

3

Thank you for your reply, Prof. Pheifer.
Actually I want to “estimate” the scaling factor \kappa_{t} during Covid periods.
(For example, Holston et al(2023) estimated \kappa_{2020} = 9.03 using US data. i.e. the variance of potential GDP of US in 2020 is about 9 times larger than pre-covid times.)

One of the observable variables in my model is log-GDP, which is non-stationary.
So I used the diffuse-filter option.
If I want to use the heteroskedastic filter option, should I stationarize the variables?

4

Estimation with stochastic volatility cannot be easily done in Dynare. Moreover, there is no smoother available for higher order solutions. The heteroskedastic_filter-option should work with any Kalman filter as before. It simply scales up the shock variance matrix.