Do lower end / cheaper rentals do better in a downturn?

[James Elden]

Question for those who have been around a while, I haven't been able to figure this out myself from research. I'm referring mainly to larger markets, say over 1 million people at least, during a housing crash / downturn where house prices go down and rental vacancy rates go up would houses in the cheapest parts of the city be less affected than the more expensive homes? My assumption was that the people in the lower end neighborhoods would have less mobility so would stay put while people that are moving out of the more expensive areas may be moving away to other cities, etc but maybe I'm completely off base. Would appreciate any input from anyone who has been around a while in real estate.