Paper simulating impact of housing policies on welfare

DSGE model simulating different housing policies in New York. Despite click-baitey title "rent control" in the paper is actually defined as AMI setasides - a percent of housing should be set aside for people below an income threshold and are limited to a certain housing size. Overall the paper finds both increased "rent control" and relaxing zoning is welfare enhancing.

Their claim is that "rent control" is welfare enhancing because it acts as insurance. But I wonder if its just because it redistributes wealth from high income earners to low income earners and if a direct wealth transfer would be more efficient. It's also surprising that in their model the housing stock barely decreases from rent control.

It's also unclear to me how immigration is handled in the model. To be a full model rents should probably change immigration rates to the city, which in turn should change the aggregative welfare calculations (and of course summing across different peoples utilities is suspect anyways). Furthermore, the initial model should be calibrated to have rents increasing faster than income in steady state since that's the motivation for rent control policies in New York/SF. And I suspect that few people argue for rent control as an insurance against negative income shocks. Though if that is indeed the main mechanism that'd be very interesting.