Does Chicago need a greenbelt?

Like many found in the UK and some in Europe? What would be the effects? Would it raise housing prices around the region artifically and make the region less welcoming to transplants? Would it just create more sprawl if expansion just went beyond the green belt? Would it make people gravitate towards the city if expansion is further cut off? Would it deter people from moving to the area in favor of sunbelt cities where sprawl is more or less welcomed?>