You may want to read Greg Morrow's UCLA dissertation on urban planning in Los Angeles for some context: http://escholarship.org/uc/item/6k64g20f#page-1

This graph (p. 3) shows that zoning changes in LA since 1960 are many orders of magnitude more important than 7,000 short-term rentals: http://1.bp.blogspot.com/-HnkwzmO56vU/VQHurofJUUI/AAAAAAAABE...