Robust standard errors (HAC) in bayesian setting

Hi,
I’m running a fixed-effect panel analysis (relationship between real exchange rate and some predictors) — full disclosure: I’m an economist… sorry. (also I’m totally Bayesian inside, but just a clumsy one outside)

When I run with plm and use robust standard errors, a number of regressors become insignificant (otherwise they are all highly significant).
I’d prefer to run the same regression with stan_glm using id’s as factors. Yet the outcome is super tight confidence bands. What should I do to correct for possible heteroskedasticity, autocorrelation and clustering?

Below some more info

# running with PLM 
fit.check<-plm(data=df.tmp,formula=form,
               effect='individual',method='within',index=c("cc","year"))
# NO VCOV CORRECTION (top regressors)
               Estimate  Std. Error  t-value  Pr(>|t|)    
M3_ratedif   0.04700513  0.00329939  14.2466 < 2.2e-16 ***
DLOIL3m     -0.04480392  0.00091979 -48.7108 < 2.2e-16 ***
VIX         -0.00126017  0.00020408  -6.1750 7.079e-10 ***
DL_PC_CDS3m -0.00951601  0.00092391 -10.2997 < 2.2e-16 ***
DCDS         0.01957848  0.00128899  15.1890 < 2.2e-16 ***
  summary(fit.pst,vcov=function(x)vcovHC(x,method="arellano", type = "HC3",cluster="group"))
               Estimate  Std. Error t-value  Pr(>|t|)    
M3_ratedif   0.04700513  0.02502063  1.8787 0.0603431 .  
DLOIL3m     -0.04480392  0.00514100 -8.7150 < 2.2e-16 ***
VIX         -0.00126017  0.00066373 -1.8986 0.0576651 .  
DL_PC_CDS3m -0.00951601  0.00162978 -5.8388 5.550e-09 ***
DCDS         0.01957848  0.01319470  1.4838 0.1379140   

# BAYESIAN ESTIMATION
fit.check2<-stan_glm(data=df.tmp,formula=update(form,'.~.+factor(cc)'),iter=10000)
mean mcse sd 10% 50% 90% n_eff Rhat
(Intercept) 2.647 0.001 0.025 2.615 2.647 2.680 1606 1.003
M3_ratedif 0.047 0.000 0.003 0.043 0.047 0.051 7429 1.000
DLOIL3m -0.045 0.000 0.001 -0.046 -0.045 -0.044 19461 1.000
VIX -0.001 0.000 0.000 -0.002 -0.001 -0.001 15896 1.000
DL_PC_CDS3m -0.010 0.000 0.001 -0.011 -0.010 -0.008 13120 1.000
DCDS 0.020 0.000 0.001 0.018 0.020 0.021 2638 1.002

OK, I got it. Coming from econometrics I totally missed the multi-level regression perspective.
I bought and read Data Analysis Using Regression and Multilevel/Hierarchical Models (Gelman and Hill) as well as Statistical Rethinking (McElreath) as well as “Regression and other stories” (Gelman, Hill and Vehtari). All beautiful (thanks).
I converted!