From my cursory analysis, "# of new housing units authorized" is by far the strongest predictor of rent & home values decreasing: https://i.imgur.com/BMsPrKY.png (r^2 = 0.47, P-value 0.000)
Nothing else ("% of housing owned by investors"?) is even close.
edit: Yes, obviously I included a time lag (3 years).
[1] https://constructioncoverage.com/research/cities-investing-m...
[2] eg, https://www.zillow.com/home-values/10221/austin-tx/#/