The author exposed the fallacy at the heart of this article in the second paragraph.
"In the United States, a large part of school funding comes from local property taxes. Each school district sets a budget and then adjusts the tax rate to cover it."
A budget gets set and then the tax rate is set based on the total property valuation in the district. If the properties in the district all go up by 10% (or 50% or 100%) it won't change the taxes at all. Each year the tax rate will be set to account for the new overall valuation (i.e. the tax rate will be lowered to adjust for higher prices). Taxes will go up if the budget increases, certainly, but not because all the property valuations have gone up. When property valuations fall, the district will set a higher tax rate to cover the budget including bonds, etc., to collect exactly whatever the budget might be.
Individual property valuation is used as a way to distribute the tax load among the various properties within the district. So, if your property valuation goes up and other property valuations don't, then your taxes will go up and everyone else's will come down a little. This is generally due to making major property improvements such as adding an addition to your house.
Bottom line, a uniform rising of valuations across a district doesn't change the amount of taxes you pay. It may drive a budget increase to cover higher salaries but that is why everyone should pay attention to the budget and stop worrying about overall valuations.
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