What is Tax Increment Financing?
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Tax increment financing is an economic development tool used in 48 states. It grew in popularity when state and federal dollars for development dried up in the 1980s.
It is intended to help property that would not develop on its own, property that would not see new growth "but for" the public investment.
Tax increment financing is intended to take blighted property, or property that is not living up to its development potential, and offer public dollars to improve the property. The public dollars might be used for demolition, streets, utilities or other improvements to make the property attractive to developers.
Specialized consultants can usually produce the evidence needed to help the property qualify for tax increment financing.
Tax increment financing involves the city borrowing money — selling bonds — to finance the improvements for the developer. The city repays those bonds by creating a special district and capturing all that district's increases in property taxes, usually for 23 years.
Taxes are also expected to slowly increase.
Here is how the "increment" and the "financing" are created...
Blighted or underdeveloped property value is expected to grow slowly over a 30-year period. 
Property values and taxes are expected to increase significantly if the development happens.
The city decides that the if derelict buildings are removed and new streets and utilities are installed, that a big box retailer will move there.
1. The city maps out a district that includes the property to be developed. It is intended to last 23 years
2. Property taxes in the district are frozen for schools and all other taxing bodies for those 23 years. 
This "increment" is used to repay the bonds.
3. For 23 years the city keeps the difference between the frozen taxes and the new taxes generated by the development.
4. After 23 years the tax increment financing has repaid the bonds and the district goes away.
5. Schools and all other taxing districts then get the new, higher share of taxes.
Property is declared blighted that would develop anyway.Schools suffer for decades and other taxes increase while we give out corporate welfare.
Property is developed that would not otherwise develop. More taxes are created than would otherwise have been available to improve our community.
Tax increment financing is prevalent but not universally loved.
That area was a prime development zone. It did not grow any faster because of the district.
The districts spur rapid growth in the majority of cases. That is why so many cities use them.
The districts hurt other businesses outside the zone, drawing businesses and shoppers to one area and away from another.
Raising commercial property values and boosting retail in one area will increase both in others.
The brown area is Belleville's Tax Increment Financing District 3.
• Property assessed at $103 million at start, currently assessed at $244 million
Example: Belleville's Tax Increment Financing District 3
• $172 million in total revenue from district
• Created in 1986. Does not expire until 2021 (35 years)
Since 1999, Belleville has spent  $30.4 million in the district. Here are some of the top expenditures:
Belleville'stax increment financing reports
Illinois tax increment financing statutes
TIF study: "A Tool for Local Economic Development"By Richard Dye and David Merriman
Illinois Tax Increment Association FAQ's
Sources, more info on tax increment financing
Illinois Comptroller tax increment financing FAQ's