Paper link: <https://www.federalreserve.gov/pubs/.../200114pap.pdf>

I have some questions on this paper, as Rigobon and Sack's writings were rather abstract as for the estimation of the beta coefficient.

On page 11, is the beta coefficient being directly estimated by plugging in constant variances? or variances are also changing in the equation?
I have tried to put the estimates from the table II on the paper, but with the assumption of constant changes in variances and covariances, I am not getting the beta estimate found by Rigobon and Sack. My beta coefficient was 0.16 whereas the coefficient on the paper was estimated to be 0.21. Anyone care to explain what is happening there? Thank you.