From a new working paper “The Price of Housing in the United States, 1890-2006” by Ronan C. Lyons, Allison Shertzer, Rowena Gray & David N. Agorastos (emphasis added):
“Zoning was adopted by almost every city in our sample during the 1920s. We see a slightly steeper gradient over the next two periods (coefficients of .48 and .29, respectively). In these periods it is possible both that the existing zoning regimes were causing higher price growth and that home price appreciation was incentivizing cities to adopt even more restrictive measures, particularly by the 1970s (Fischel, 2015; Molloy et al., 2020). The gradient in the final period (1980-2006) is even steeper, however (coefficient of .67), suggesting a closer relationship between zoning and home price appreciation towards the end of the 20th century.”
The authors acknowledge that they cannot establish causality with their data, but this is consistent with existing research, such as a paper by Gyourko and Krimmel that I previously discussed.
Economist Writing Every Day 