A recent UCLA study found that developers provided more housing in new housing developments when parking requirements were eliminated. Relaxed parking requirements also freed developers to provide different types of housing, including housing in older buildings, in previously disinvested areas, and housing marketed toward non-drivers.
To learn more: http://la.curbed.com/archives/2013/04/lack_of_parking_requirements_led_to_cheaper_housing_in_dtla.php