At the two highest ranked Econ Phd programs (MIT, Harvard), the following has been necessary - but certainly not always sufficient:
Outstanding econ background + advanced math including Real Analysis or higher with near perfect grades in both subjects.
Near perfect GRE scores.
Extremely laudatory LORs from professors known to and respected by the admissions committees.
2 years post grad RA experience at a Central Bank or top level Econ program.
UChicago has always been very quant, and will take math majors with less of an econ background, but while a top 10 program it’s not in the same league as the two in Cambridge.