This paper was discussed in another forum, and people raised that point.
However, it was also pointed out that this paper isn't really about supply, it's about supply regulation and supply constraints:
"... We also use the measures of the Wharton Residential Land Use Regulatory Index (WRLURI) by Gyourko et al. (2008), generated at the MSA-level by Saiz (2010), which capture variation in the regulatory environment across MSAs. We multiply this index by minus one so that increases in the value indicate a less restrictive regulatory environment and so, ostensibly, a more elastic housing supply function."
You could eliminate housing supply regulations and still have poor housing supply for other reasons.
However, it was also pointed out that this paper isn't really about supply, it's about supply regulation and supply constraints:
"... We also use the measures of the Wharton Residential Land Use Regulatory Index (WRLURI) by Gyourko et al. (2008), generated at the MSA-level by Saiz (2010), which capture variation in the regulatory environment across MSAs. We multiply this index by minus one so that increases in the value indicate a less restrictive regulatory environment and so, ostensibly, a more elastic housing supply function."
You could eliminate housing supply regulations and still have poor housing supply for other reasons.