If teacher pay made a big difference in outcomes, expensive private schools would have very well paid teachers. But private schools typically have lower teacher pay than public schools.
Teacher pay doesn't have as large an influence on student success as it does on how many people are willing to enter the occupation and stay there. Private school teachers typically deal with far fewer students in the classroom and in much better conditions. They also don't typically have to spend as much of their own money on basic school supplies. Improving conditions at public schools and lowering classroom sizes would help to attract teachers too.
Washington state has the highest public school teacher pay in the country (over 100k/yr). It also has educational outcomes which are middle of the pack. That correlation doesn't hold in many cases. Oh, and the fact that half of the funding for the district goes to administration doesn't help either.
You need to have both. Training/credentialing and pay. Just one is insufficient.
Longer/better educator training both increases skills/outcomes and is a gate for the poorly-suited. Higher pay makes the training seem worthwhile and increases stickiness/tenure.
