Rigobon and Sack 2003 "Measuring the reaction of monetary policy to the stock market" - Replicate

Paper link: https://www.federalreserve.gov/pubs/feds/2001/200114/200114pap.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 changes in variances and covariances across regimes? or variances/covariances within each regime are also changing in the equation?

I have tried to put the estimates from the table II on the paper, but by assuming constant changes in variances and covariances across regimes, I am not getting the beta estimate found by Rigobon and Sack. My beta coefficient is becoming 0.16 whereas the coefficient on the paper was estimated to be 0.21. I greatly appreciate any help. Thank you.

Sorry, but this is a forum dedicated to Dynare and DSGE modeling. I am afraid you won’t find an answer here for a question that far away from these topics.