Dagney Faulk and Mike Hicks at Ball State’s Center for Business and Economic Research have written another excellent study of Indiana property taxes.

This one’s about assessment quality. It compares thousands of homes to see if their assessed values match their sales prices, as they should in our “market value in use” system. Search for the center, click Current Studies, and you’ll find it.

The study uses some standard measures of assessment quality. The sales ratio divides the assessed value by the sales price. Since the assessment should match the sales price, the sales ratio ought to be near one.

Assessment experts like anything between 0.9 and 1.1. Indiana’s average sales ratio in 2012 was 1.065, so that’s pretty good.

The coefficient of dispersion (COD) measures variation around the sales ratio, to see if each property’s ratio is close to one. A COD less than 15 is good. Indiana’s statewide number is 16.5. Close, but not quite there.

The study’s headline, though, is about assessments of higher- and lower-valued homes. Higher-valued homes tend to be under-assessed and lower-valued homes tend to be over-assessed. Owners of expensive homes are getting a tax break and owners of cheaper homes are paying too much.

Another study reached the same conclusion. Indiana University alumnus Olha Krupa published a paper in Public Finance Review last year, also looking at Indiana assessment practices. She found the same over/under inequity. Two studies, same result. We may have a problem here.

Fixing the problem would improve equity, but what about revenue? Based on Ball State’s sales ratios and data on homesteads by assessed value, it looks like fixing the over/under problem would reduce total homestead assessed values by 2 to 3 percent. The loss from cutting assessments on low-valued homes would outweigh the gain from raising assessments on high-valued homes.

Now here’s a chance to play with that Rubik’s Cube of Indiana local government, the constitutional property tax caps. Lower total assessed value means higher tax rates, because it takes higher rates to raise the same revenue.

Higher tax rates mean that more taxpayers hit their tax caps. Fixing the over/under problem could reduce local government revenue.

But there’s more — the Rubik’s Cube never disappoints. Take two houses, a cheaper one with a selling price of $100,000 and a more expensive home priced at $250,000. Suppose the assessments are off by $10,000 each, with the cheaper home over-assessed at $110,000 and the expensive one under-assessed at $240,000. The sales ratio of the cheaper home is 1.1. It’s over-assessed by 10 percent. The sales ratio of the expensive home is 0.96, under-assessed by 4 percent. Those ratios are pretty close to Faulk and Hicks’ actual results.

Before the tax caps, fixing this assessment inequity might not have affected local revenues. That’s still true where tax rates are low. With the caps and higher tax rates, though, it looks like the fix could reduce revenue.

Let’s put these homes in a rural district with a tax rate of $1.50 per $100 assessed value, a typical rate where there’s no city or town. After the standard, supplemental and mortgage deductions, the over-assessment adds $98 to the cheaper home’s tax bill, and the under-assessment subtracts $98 from the expensive home’s bill. Fixing the over/under problem would not change total assessed value, since we’d add $10,000 to one and subtract it from the other. The tax rate wouldn’t change, and tax bill changes would cancel out.

Now put the homes in a city district with a typical rate of $2.50. The cheaper home pays $163 more at the higher tax rate, due to the $10,000 over-assessment. But the under-assessed expensive home’s bill is just $100 less. Fixing the over/under problem leaves total assessed value unchanged, but local governments see a net revenue loss, gaining $100 but losing $163. Why?

Because with a rate of $2.50 the high-valued home is at its tax cap. Raising its assessment from $240,000 to $250,000 increases the 1 percent cap amount from $2,400 to $2,500. The homeowner pays the extra $100. The cheaper home is below its tax cap. Fixing the $10,000 over-assessment reduces taxable assessed value by $6,500, after the 35 percent supplemental deduction. At the $2.50 tax rate, that’s $163 less.

Before the tax caps, fixing this assessment inequity might not have affected local revenues. That’s still true where tax rates are low. With the caps and higher tax rates, though, it looks like the fix could reduce revenue.

Larry DeBoer is professor of agricultural economics at Purdue University. Send comments to [email protected].

Larry DeBoer is professor of agricultural economics at Purdue University. Send comments to [email protected].