Okay I think I understand what happened. A couple posts ago you listed to an executive summary for CASPEH. I don't believe you've ever read the complete report, which is around 96 pages.
If you dig into the details, you'll actually find out that all of your assumptions are spoken about in terms of coming out with a reasonable amount of hours worth inside a California based upon the survey data from this research. The detailed report includes the following:
Median monthly household income in the six months before homelessness: $960 (all participants), $950 for non‑leaseholders, $1,400 for leaseholders. State the obvious if the weighted average is 960 and you have two groups, you can run the math to show that the non-lease holders were 98% of the sample.
Why we do want to think about Least Holders in reality is the renters where 98% of the problems exist. This is a clear application of the Pareto Principle, and so we should look at renters as the core of the homeless issue.
Median monthly housing cost: $200 for non‑leaseholders (0 for many), $700 for leaseholders. Of non-leaseholders, 43% were not paying any rent; among those who reported paying anything, the median monthly rent was $450.
In essence, if you look at the details you'll see where you're assuming are a lot of assumptions are actually somewhat addressed by the detailed report. Unfortunately, I'm going to suggest the detailed report is pretty shabby in terms of forcing somebody to dig out a lot of information which they should offer in some sort of a downloadable table for analysis.
Computationally, we can therefore figure out the minimal amount of hours these people must have been working based on the fact that they must have made at least minimum wage in the state of California.
There's not a lot of assumptions in this. It's based upon the detailed survey data and utilizing California minimal wage, which is where the survey was taken. The issue is digging into the details and computationally extracting information and assumptions that is not blinded by our own biases walking into something.
Again, there is excellent work out of University of Washington to suggest that higher housing costs lends itself toward greater rates of homelessness. That's not under debate here. The issue is from the survey data, it's very reasonable to do some basic computation to put some parameters around the data. It's not assumption, it's critical thinking.
You may be confusing jameslk with me - I'm actually the one who linked the CASPEH exec summary. Your underemployment math is interesting, but I'd note the study also reports 34% have limitations in daily activities, 22% mobility limitations, 70% haven't worked 20+ hours weekly in 2+ years. When asked why, participants cited disability, age, transportation, and lack of housing itself as barriers. So the causation may be more circular than "fix jobs first" as the same factors driving underemployment are driving housing instability, and being unsheltered makes holding a job harder.